SECURITY ANALYSIS AND
PORTFOLIO MANAGEMENT
Second Edition
S. KEVIN
Director, Bishop Jerome Institute, Kollam, Kerala
Formerly, Pro-Vice-Chancellor and Professor of Commerce
University of Kerala
Delhi-110092
2015
SECURITY ANALYSIS AND PORTFOLIO MANAGEMENT, Second Edition
S. Kevin
© 2015 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be
reproduced in any form, by mimeograph or any other means, without permission in writing from the
publisher.
ISBN-978-81-203-5130-1
The export rights of this book are vested solely with the publisher.
Thirteenth Printing (Second Edition)
...
...
...
July, 2015
Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj
Industrial Estate, Delhi-110092 and Printed by Mudrak, 30-A, Patparganj, Delhi-110091.
To
My beloved parents
Stephen and Mary
Table of Contents
Preface
1. Introduction
What is Portfolio Management
Phases of Portfolio Management
Securities Market
Security Analysis
Portfolio Analysis
Portfolio Selection
Portfolio Revision
Portfolio Evaluation
Evolution of Portfolio Management
Role of Portfolio Management
Financial Derivatives
Review Questions
References
2. Investment
Meaning of Investment
Financial and Economic Meaning of Investment
Characteristics of Investment
Objectives of Investment
Investment vs Speculation
Investment vs Gambling
Types of Investors
Investment Avenues
Summary
Review Questions
References
3. Securities Market
Financial Market
Segments of Financial Market
Types of Financial Market
Participants in the Financial Market
Regulatory Environment
Primary Market/New Issues Market
Methods of Floating New Issues
Principal Steps in Floating a Public Issue
Book Building
Role of Primary Market
Regulation of Primary Market
Review Questions
References
4. Stock Exchanges
What is a Stock exchange
Functions of Stock Exchanges
Stock Market in India
Over the Counter Exchange of India (OTCEI)
National Stock Exchange of India (NSE)
Inter-connected Stock Exchange of India (ISE)
MCX-SX: The newest stock exchange of the country
SX40—The market index of MCX-SX
Organisation, Membership and Management of Stock Exchanges
Listing of Securities
Permitted Securities
Regulation of Stock Exchanges
Review Questions
5. Trading System In Stock Exchanges
Trading System
Types of Orders
Settlement
Speculation
Types of Speculators
Margin Trading
Depositories
Stock Market Quotations And Indices
Review Questions
6. Risk
Meaning of Risk
Elements of Risk
Systematic Risk
Unsystematic Risk
Measurement of Risk
Measurement of Systematic Risk
Value at Risk (VaR) analysis
Origin
Concept
Methods
Evaluation
Solved Examples
Exercises
Review Questions
References
7. Fundamental Analysis: Economy Analysis
Meaning of Fundamental Analysis
Economy-Industry-Company Analysis Framework
Economy Analysis
Economic Forecasting
Forecasting Techniques
Anticipatory Surveys
Barometric or Indicator Approach
Econometric Model Building
Opportunistic Model Building
Review Questions
References
8. Industry and Company Analysis
Industry Analysis
Concept of Industry
Industry Life Cycle
Industry Characteristics
Company Analysis
Financial Statements
Analysis of Financial Statements
Other Variables
Assessment of Risk
Review Questions
References
9. Share Valuation
Concept of Present value
Share Valuation Model
One Year Holding Period
Multiple-year Holding Period
Constant Growth Model
Multiple Growth Model
Discount rate
Multiplier Approach to Share Valuation
Regression analysis
Solved Examples
Exercises
Review Questions
10. Bond Valuation
Bond Returns
Coupon Rate
Current Yield
Spot Interest Rate
Yield to Maturity (YTM)
Yield to Call (YTC)
Bond Prices
Bond Pricing theorems
Bond Risks
Default Risk
Interest Rate Risk
Bond Duration
Solved Examples
Exercises
Review Questions
References
11. Technical ANalysis
Meaning of technical analysis
Dow Theory
Basic principles of Technical Analysis
Price Charts
Trends and Trend Reversals
Chart Patterns
Support and Resistance
Reversal Patterns
Continuation Patterns
Elliot wave theory
Mathematical Indicators
Moving Averages
Oscillators
Market Indicators
Breadth of the Market
Short Interest
Odd-lot Index
Mutual Fund Cash Ratio
Technical Analysis vs Fundamental Analysis
Review Questions
12. Efficient Market Theory
Random Walk Theory
The Efficient Market Hypothesis
Forms of Market Efficiency
Empirical Tests of Weak Form Efficiency
Empirical Tests of Semi-strong Form Efficiency
Tests of Strong Form Efficiency
EMH vs Fundamental and Technical Analyses
Competitive Market Hypothesis
Review Questions
References
13. Portfolio Analysis
Expected Return of a portfolio
Risk of a Portfolio
Reduction of portfolio risk through diversification
Security Returns Perfectly Positively Correlated
Security Returns Perfectly Negatively Correlated
Security Returns Uncorrelated
Portfolios with more than two securities
Risk-Return Calculations of Portfolios with more than two
securities
Solved Examples
Exercises
Review Questions
14. Portfolio Selection
Feasible set of portfolios
Efficient Set of Portfolios
Selection of Optimal Portfolio
Limitations of Markowitz Model
Single Index Model
Measuring Security Return and Risk under Single Index Model
Measuring Portfolio Return and Risk under Single Index Model
Multi-Index Model
Solved Examples
Exercises
Review Questions
References
15. Capital Asset Pricing Model (CAPM)
Fundamental Notions of Portfolio Theory
Assumptions of CAPM
Efficient Frontier with Riskless Lending and Borrowing
The Capital Market Line
The Security Market Line
CAPM
SML and CML
Pricing of Securities with CAPM
Solved Examples
Exercises
Review Questions
16. Arbitrage Pricing Theory (APT)
The return generating model
Factors affecting stock return
Expected return on stock
An Illustration
Asset pricing and arbitrage
Conclusion on APT
APT and CAPM
Solved Examples
Exercises
Review Questions
17. Portfolio Revision
Need for Revision
Meaning of Portfolio Revision
Constraints in Portfolio Revision
Portfolio revision Strategies
Formula Plans
Constant Rupee Value Plan
Constant Ratio Plan
Dollar Cost Averaging
Review Questions
18. Portfolio Evaluation
Need for Evaluation
Evaluation Perspective
Meaning of Portfolio Evaluation
Measuring Portfolio Return
Risk Adjusted Returns
Differential Return
Decomposition of Performance
Solved Examples
Exercises
Review Questions
19. Financial Derivatives
What are financial Derivatives
Forwards
Hedging of foreign exchange risk through currency forwards
Advantages of Forward Contracts
Disadvantages of forwards
Review Questions
References
20. Futures
Futures Contracts
The Asset
Delivery Terms
Price and Price Limits
Long and Short Positions and Open Interest
Features of Futures Contracts
Organised Exchange
Standardised Terms
Clearing House
Margin System
Closing of Futures
Index Futures
Hedging
Imperfection in Hedging
Speculation
Index Futures Trading in India
Review Questions
References
21. Options
Stock Options (Options on Shares)
Call Options
Specifications of Stock Options
Option Prices in the Newspapers
Trading in call options
Profit and Loss of a Call Option Writer
Determinants of the Option Premium
Put options
Closing out of Options
Uses of Options
Hedging the Value of a Stockholding
Protecting Profit Accrued on Share
Hedging Anticipated Purchases
Additional Income from Stockholding
Speculative Profit from Options Trading
Review Questions
References
22. Option pricing
The Black-Scholes Model
Factors Affecting Option Prices
Assumptions
Notations
The Pricing Formulas
Use of Statistical Tables
Solved Examples
Calculation of Put Option Price using Put-call Parity
Dividends Anticipated during the Life of an Option
Pricing of American Options
Binomial Model of Option Pricing
The Model
The Case of the American Option
The Black-Scholes model and the Binomial model— a contrast
Exercises
Review Questions
Appendix
Glossary
Bibliography
Index
PREFACE
Investment in securities and other capital market instruments is a popular
method of wealth creation. The investment is expected to generate return in
the future; but there is also an amount of risk inherent in every investment.
Thus, return and risk are the two important characteristics of investment.
Wealth creation requires that the investor should maximize the return from
investment, while minimizing the risk involved in it. One of the methods of
minimizing risk is diversification of investment through the creation of a
portfolio of different types of securities. But, any random portfolio of
securities will not be of much use in minimizing risk. The investor has to
identify the particular portfolio that will maximize the return and minimize
the risk. This portfolio is described as the ‘optimal portfolio’. Identifying the
optimal portfolio, creating that portfolio, revising the portfolio to ensure that
it continues to be optimal and finally evaluating the performance of the
portfolio—these activities have to be performed in a systematic and
disciplined manner. The planning and execution of these activities is
described as portfolio management.
Wealth creation through investment in securities involves two different
phases, namely, Security Analysis and Portfolio Management. Security
analysis helps to identify the securities that have good potential for growth.
Portfolio management process concentrates on managing the optimal
portfolio identified and created with the securities already identified as
having growth potential. Portfolio management is the traditional method used
to minimize the risk in investment activity.
Risk reduction in investment is now possible with the use of derivative
instruments which are of recent origin. A derivative instrument helps to
hedge the risk involved in the trading of an underlying asset which may be a
physical commodity or a financial asset. Thus, the risk involved in the trading
of securities can be hedged with the help of a derivative instrument.
Forwards, futures, options and swaps are the basic derivative instruments.
Derivatives are innovative instruments of recent origin and derivatives
trading is a novel practice.
The first edition of this book was written with the objective of explaining in
detail the processes of security analysis and portfolio management and giving
an introduction to derivative instruments and derivatives trading. The book
has been well received by the academic community of teachers and students
and also by the investing community. During the period of nine years since
the publication of the first edition in 2006, there have been twelve reprints of
the book, indicating its continuing demand. Hence, the wide acceptance of
the text has been the motivation for bringing out the second edition.
However, the basic structure of the book has been retained as such in this
second edition. Two new chapters on Arbitrage Pricing Theory (APT) and
Option Pricing have been introduced; two new sections on MCX-SX and
Value at Risk (VaR) Analysis have also been added. Also, a Glossary of
important terms used in the book has been appended.
I humbly present this Second Edition of the book before the academic and
investing community.
The readers can contact me at kevinide@gmail.com or phi@phindia.com.
S. Kevin
INTRODUCTION
Investing in securities such as shares, debentures and bonds is profitable as
well as exciting. It is indeed rewarding, but involves a great deal of risk and
calls for scientific knowledge as well as artistic skill. In such investments,
both rational as well as emotional responses are involved. Investing in
financial securities is now considered to be one of the best avenues for
investing one’s savings while it is acknowledged to be one of the most risky
avenues of investment.
It is rare to find investors investing their entire savings in a single security.
Instead, they tend to invest in a group of securities. Such a group of securities
is called a portfolio. Creation of a portfolio helps to reduce risk without
sacrificing returns. Portfolio management deals with the analysis of
individual securities as well as with the theory and practice of optimally
combining securities into portfolios. An investor who understands the
fundamental principles and analytical aspects of portfolio management has a
better chance of success.
WHAT IS PORTFOLIO MANAGEMENT
An investor considering investment in securities is faced with the problem of
choosing from among a large number of securities. His choice depends upon
the risk-return characteristics of individual securities. He would attempt to
choose the most desirable securities and like to allocate his funds over this
group of securities. Again he is faced with the problem of deciding which
securities to hold and how much to invest in each. The investor faces an
infinite number of possible portfolios or groups of securities. The risk and
return characteristics of portfolios differ from those of individual securities
combining to form a portfolio. The investor tries to choose the optimal
portfolio taking into consideration the risk-return characteristics of all
possible portfolios.
As the economic and financial environment keeps changing, the risk-return
characteristics of individual securities as well as portfolios also change. This
calls for periodic review and revision of investment portfolios of investors.
An investor invests his funds in a portfolio expecting to get a good return
consistent with the risk that he has to bear. The return realised from the
portfolio has to be measured and the performance of the portfolio has to be
evaluated.
It is evident that rational investment activity involves creation of an
investment portfolio. Portfolio management comprises all the processes
involved in the creation and maintenance of an investment portfolio. It deals
specifically with security analysis, portfolio analysis, portfolio selection,
portfolio revision and portfolio evaluation. It also makes use of analytical
techniques of analysis and conceptual theories regarding rational allocation of
funds. Portfolio management is a complex process which tries to make
investment activity more rewarding and less risky.
PHASES OF PORTFOLIO MANAGEMENT
Portfolio management is a process encompassing many activities aimed at
optimising the investment of one’s funds. Five phases can be identified in this
process:
1. Security analysis
2. Portfolio analysis
3. Portfolio selection
4. Portfolio revision
5. Portfolio evaluation
Each phase is an integral part of the whole process and the success of
portfolio management depends upon the efficiency in carrying out each of
these phases.
Securities Market
Investment in securities involves buying and selling of securities.
Construction of a portfolio and its periodic revision require several such
transactions of buying and selling securities. These transactions have to be
carried out in the securities market, which is the market where trading in
securities takes place. Investors may directly purchase securities from the
company when it is issuing securities. To issue new securities, companies go
through several steps and use services of different intermediaries such as
merchant bankers, share transfer agents, registrars to the issue, bankers to the
issue, underwriters, brokers, etc.
Securities already issued by companies are traded between investors in the
stock exchanges, which constitute the secondary market for securities. Stock
exchanges provide liquidity to the investments made in the corporate sector.
They also provide valuation of the securities of different companies listed in
the stock exchanges for trading. There are two national level stock exchanges
in the country—the National Stock Exchange of India (NSE) and the Stock
Exchange, Mumbai (BSE), and several regional stock exchanges located in
different parts of the country.
The functioning of stock exchanges is regulated by certain Acts, rules,
regulations, by-laws and guidelines so as to ensure fair and transparent
processes in all their transactions. The Securities and Exchange Board of
India (SEBI) acts as the regulator for both the primary and secondary markets
in India, supervising and monitoring their functioning in every respect.
A stock exchange is primarily a market for trading in securities. But it is a
market with several peculiar features and is quite unlike other ordinary
markets we are familiar with. The trading system in a stock exchange,
including placing of orders, execution of orders, exchange of cash and
securities between the trading parties, etc. is unique. It has been evolved and
reformed over the years to ensure an efficient and transparent trading
mechanism.
The continuous fluctuations in the prices of securities lead to speculative
activities in stock exchanges. An understanding of the different types of
speculative activities and the speculators is useful in studying the price
movements in stock exchanges. The stock market indices indicate the
direction of market movements.
Security Analysis
The securities available to an investor for investment are numerous and of
various types. The shares of over 7000 companies are listed in the stock
exchanges of the country. Traditionally, the securities were classified into
ownership securities such as equity shares and preference shares and
creditorship securities such as debentures and bonds. Recently a number of
new securities with innovative features are being issued by companies to
raise funds for their projects. Convertible Debentures, Deep Discount Bonds,
Zero Coupon Bonds, Flexi Bonds, Floating Rate Bonds, Global Depository
Receipts, Euro-currency Bonds, etc. are some of these new securities. From
this vast group of securities the investor has to choose those securities which
he considers worthwhile to be included in his investment portfolio. This calls
for a detailed analysis of the available securities.
Security analysis is the initial phase of the portfolio management process.
This step consists of examining the risk-return characteristics of individual
securities. A basic strategy in securities investment is to buy underpriced
securities and sell overpriced securities. But the problem is how to identify
underpriced and overpriced securities, or, in other words, ‘mispriced’
securities. This is what security analysis is all about.
There are two alternative approaches to security analysis, namely
fundamental analysis and technical analysis. They are based on different
premises and follow different techniques. Fundamental analysis, the older
of the two approaches, concentrates on the fundamental factors affecting the
company such as the EPS of the company, the dividend pay-out ratio, the
competition faced by the company, the market share, quality of management,
etc. A fundamental analyst studies not only the fundamental factors affecting
the company, but also the fundamental factors affecting the industry to which
the company belongs as also the economy fundamentals.
According to this approach, the share price of a company is determined by
these fundamental factors. The fundamental analyst works out the true worth
or intrinsic value of a security based on its fundamentals; then compares this
intrinsic value with the current market price. If the current market price is
higher than the intrinsic value, the share is said to be overpriced and vice
versa. The mispricing of securities provides an opportunity to the investor to
acquire the share or dispose of the share profitably. An investor would buy
those securities which are underpriced and sell those securities which are
overpriced. It is believed that notable cases of mispricing will be corrected by
the market in future. Prices of undervalued shares will increase and those of
overvalued shares will decline.
Fundamental analysis helps to identify fundamentally strong companies
whose shares are worthy to be included in the investor’s portfolio.
The second alternative approach to security analysis is technical analysis. A
technical analyst believes that share price movements are systematic and
exhibit certain consistent patterns. He, therefore, studies past movements in
the prices of shares to identify trends and patterns. He then tries to predict the
future price movements. The current market price is compared with the future
predicted price to determine the extent of mispricing. Technical analysis is an
approach which concentrates on price movements and ignores the
fundamentals of the shares.
A more recent approach to security analysis is the efficient market
hypothesis. According to this school of thought, the financial market is
efficient in pricing securities. The efficient market hypothesis holds that
market prices instantaneously and fully reflect all relevant available
information. It means that the market prices of securities will always equal
their intrinsic values. As a result, fundamental analysis which tries to identify
undervalued or overvalued securities is said to be a futile exercise.
The efficient market hypothesis further holds that share price movements are
random and not systematic. Consequently, technical analysis which tries to
study price movements and identify patterns in them is of little use.
Efficient market hypothesis is a direct repudiation of both fundamental
analysis and technical analysis. An investor cannot consistently earn
abnormal returns by undertaking fundamental analysis or technical analysis.
According to efficient market hypothesis, it is possible for an investor to earn
normal returns by randomly choosing securities of a given risk level.
Portfolio Analysis
A portfolio is a group of securities held together as investment. Investors
invest their funds in a portfolio of securities rather than in a single security
because they are risk averse. By constructing a portfolio, investors attempt to
spread risk by not putting all their eggs into one basket. Thus, diversification
of one’s holdings is intended to reduce risk in investment.
Security analysis provides the investor with a set of worthwhile or desirable
securities. From this set of securities an indefinitely large number of
portfolios can be constructed by choosing different sets of securities and also
by varying the proportion of investment in each security. Each individual
security has its own risk-return characteristics which can be measured and
expressed quantitatively. Each portfolio constructed by combining the
individual securities has its own specific risk and return characteristics which
are not just the aggregates of the individual security characteristics. The
return and risk of each portfolio has to be calculated mathematically and
expressed quantitatively.
Portfolio analysis phase of portfolio management consists of identifying the
range of possible portfolios that can be constituted from a given set of
securities and calculating their return and risk for further analysis.
Portfolio Selection
Portfolio analysis provides the input for the next phase in portfolio
management which is portfolio selection. The goal of portfolio construction
is to generate a portfolio that provides the highest returns at a given level of
risk. A portfolio having this characteristic is known as an efficient portfolio.
The inputs from portfolio analysis can be used to identify the set of efficient
portfolios. From this set of efficient portfolios, the optimal portfolio has to be
selected for investment. Harry Markowitz’s portfolio theory provides both
the conceptual framework and the analytical tools for determining the optimal
portfolio in a disciplined and objective way.
Portfolio Revision
Having constructed the optimal portfolio, the investor has to constantly
monitor the portfolio to ensure that it continues to be optimal. As the
economy and financial markets are dynamic, changes take place almost daily.
As time passes, securities which were once attractive may cease to be so.
New securities with promises of high returns and low risk may emerge. The
investor now has to revise his portfolio in the light of the developments in the
market. This revision leads to purchase of some new securities and sale of
some of the existing securities from the portfolio. The mix of securities and
their proportion in the portfolio changes as a result of the revision.
Portfolio revision may also be necessitated by some investor-related changes
such as availability of additional funds, change in risk attitude, need of cash
for other alternative use, etc.
Whatever be the reason for portfolio revision, it has to be done scientifically
and objectively so as to ensure the optimality of the revised portfolio.
Portfolio revision is not a casual process to be carried out without much care.
In fact, in the entire process of portfolio management, portfolio revision is as
important as portfolio analysis and selection.
Portfolio Evaluation
The objective of constructing a portfolio and revising it periodically is to earn
maximum returns with minimum risk. Portfolio evaluation is the process
which is concerned with assessing the performance of the portfolio over a
selected period of time in terms of return and risk. This involves quantitative
measurement of actual return realised and the risk born by the portfolio over
the period of investment. These have to be compared with objective norms to
assess the relative performance of the portfolio. Alternative measures of
performance evaluation have been developed for use by investors and
portfolio managers.
Portfolio evaluation is useful in yet another way. It provides a mechanism for
identifying weaknesses in the investment process and for improving these
deficient areas. It provides a feedback mechanism for improving the entire
portfolio management process.
The portfolio management process is an ongoing process. It starts with
security analysis, proceeds to portfolio construction, and continues with
portfolio revision and evaluation. The evaluation provides the necessary
feedback for designing a better portfolio next time. Superior performance is
achieved through continual refinement of portfolio management skills.
EVOLUTION OF PORTFOLIO MANAGEMENT
Portfolio management is essentially a systematic method of managing one’s
investments efficiently. Many factors have contributed to the development
and growth of this systematic approach to investment management. It would
be interesting to trace the evolution of investment management through the
years.
In the early years of this century analysts used financial statement data for
evaluating the worth of securities of companies. This started with the analysis
of railroad securities in U.S.A. A booklet entitled The Anatomy of a Railroad
Report was published by Thomas F. Woodlock in 1900. It was regarded as a
classic in railroad analysis. Financial statement analysis became more popular
in the investment field, although most writers on investment were not clear
about the procedure to be adopted. They generally advocated the calculation
and use of certain financial ratios for the purpose. John Moody in his book
The Art of Wall Street Investing, published in 1906, strongly supported
financial statement analysis for investment purposes. Lawrence Chamberlain,
in his book The Principles of Bond Investment which was published in 1911,
proposed an analysis which later came to be known as common-size
analysis.1
During the early part of this century another group of analysts concentrated
their attention on the behaviour of the stock market. Their investment strategy
consisted in studying the stock price movements with the help of price charts.
This method came to be known as technical analysis. It evolved during
1900−1902 when Charles H. Dow, the founder of the Dow Jones and Co.,
presented his views in a series of editorials in the Wall Street Journal in
U.S.A. The advocates of technical analysis believed that stock price
movement was orderly and systematic and that definite patterns could be
identified in these movements. Their investment strategies were built around
the identification of trends and patterns in stock price movements.
Another prominent author who supported technical analysis was Ralph N.
Elliot who published a book in 1938 entitled The Wave Principle. After
analysing seventy five years of share price data, he concluded that the market
movement was quite orderly and followed a pattern of waves. His theory has
come to be known as the Elliot Wave Theory.
According to J.C. Francis2, the development of investments management can
be traced chronologically through three different phases.
The first phase could be characterised as the speculative phase. Investment
was not a widespread activity; it was carried on only by the wealthy;
moreover, it was of a speculative nature. Investment management was an art
and needed skill. Price manipulation was resorted to by the investors. During
this time ‘pools’ and ‘corners’ were used for manipulation. All these led to
the stock exchange crash in 1929. Finally, the daring speculative ventures of
investors were made illegal in the United States by the Securities Act of
1934.
During the 1930s investments management entered its second phase, a phase
of professionalism. After the first US regulations governing investment
trading were passed in 1933−34, the investment industry began the process of
upgrading its ethics, establishing standard practices and generating a good
public image. As a result the investment markets became safer places and
ordinary people began to invest. Investors began to analyse the securities
seriously before undertaking investments.
During this period the research work of Benjamin Graham and David L.
Dodd was widely publicised and publicly acclaimed. They published the
results of their research in a book titled Security Analysis in 1934. This was
considered the first major work in the field of security analysis and laid the
ground work for the security analysis profession. They are considered
pioneers of security analysis as a discipline.
Investments management has now entered its third phase, the scientific
phase. The publication of a paper on portfolio selection in the Journal of
Finance in 1952 by Harry Markowitz, marked the beginning of this third
phase. The foundations of Modern Portfolio Theory were laid by Markowitz.
His pioneering work on portfolio management is described in his 1952 article
in the Journal of Finance and in the subsequent book published in 1959 titled
Portfolio Selection: Efficient Diversification of Investments.
Markowitz attempted to quantify risk. He showed how the risk in investment
could be reduced through proper diversification of investment which required
the creation of a portfolio. He provided analytical tools for the analysis and
selection of the optimal portfolio. This pioneering portfolio approach to
investments management won him the Nobel prize for economics in 1990.
The work done by Markowitz was extended by William Sharpe, John Lintner
and Jan Mossin through the development of the capital asset pricing model
(CAPM). In fact, Sharpe shared the Nobel prize for economics in 1990 with
Markowitz and Miller, for his contribution to the development of CAPM.
The developments in the field of portfolio management are continuing apace.
In fact, the last two phases in the development of portfolio management
practice, namely professionalism and scientific analysis, are currently
advancing simultaneously.
ROLE OF PORTFOLIO MANAGEMENT
There was a time when portfolio management was an exotic term, an elite
practice beyond the reach of ordinary people, in India. The scenario has
changed drastically. Portfolio management is now a familiar term and is
widely practised in India. The theories and concepts relating to portfolio
management now find their way to the front pages of financial newspapers
and the cover pages of investment journals in India.
In the beginning of the nineties India embarked on a programme of economic
liberalisation and globalisation. This reform process has made the Indian
capital markets active. The Indian stock markets are steadily moving towards
higher efficiency, with rapid computerisation, increasing market
transparency, better infrastructure, better customer service, closer integration
and higher volumes. The markets are dominated by large institutional
investors with their diversified portfolios. A large number of mutual funds
have been set up in the country since 1987. With this development,
investment in securities has gained considerable momentum.
Along with the spread of securities investment among ordinary investors, the
acceptance of quantitative techniques by the investment community changed
the investment scenario in India. Professional portfolio management, backed
by competent research, began to be practised by mutual funds, investment
consultants and big brokers. The Securities and Exchange Board of India
(SEBI), the stock market regulatory body in India, is supervising the whole
process with a view to making portfolio management a responsible
professional service to be rendered by experts in the field.
With the advent of computers the whole process of portfolio management has
become quite easy. The computer can absorb large volumes of data, perform
the computations accurately and quickly give out the results in any desired
form. Moreover, simulation, modelling etc. provide means of testing
alternative solutions.
The trend towards liberalisation and globalisation of the economy has
promoted free flow of capital across international borders. Portfolios now
include not only domestic securities but also foreign securities.
Diversification has become international. In this context, financial
investments cannot be conceived of without portfolio management.
Another significant development in the field of investment management is
the introduction of derivative securities such as options and futures. The
trading in derivative securities, their valuation, etc. have broadened the scope
of investment management.
Investment is no longer a simple proccess. It requires scientific knowledge, a
systematic approach and also professional expertise. Portfolio management
which combines all these elements is the method of achieving efficiency in
investment.
Financial Derivatives
Investment in securities is inherently risky because of the volatility in the
price movements of securities. This volatility creates uncertainty regarding
future price movements. This, in turn, exposes the investors to risk. Since
investors are likely to suffer losses on account of the uncertain future price
movements, they like to avoid such risk, or at least, to minimize such risk.
Financial derivatives have evolved as a mechanism for reducing or hedging
the risk involved in financial investments. Futures and options are the most
common derivative instruments. Each derivative instrument has as underlying
asset such as a security, a foreign currency, etc. whose price fluctuations can
be hedged by trading in the derivatives market. An investor buying or selling
a financial asset can reduce the risk involved by simultaneously trading in the
derivative instrument. Thus, investment in securities can be profitably
combined with derivatives trading to achieve the objectives of maximizing
returns and minimizing risk.
Futures
The uncertainty regarding the future price movement of shares, foreign
currencies, etc. can be managed by entering into “futures contracts”. A
futures contract is essentially an agreement to buy or sell an underlying
asset such as a security or foreign currency at a certain time in the future for a
predetermined price. Such a contract effectively eliminates the uncertainty
regarding the future price of the underlying asset to be traded in the future.
Futures contracts are regularly traded in futures exchanges. The assets
underlying futures contracts may be financial assets such as shares, foreign
currencies, etc., or commodities such as wheat, coffee, gold, petroleum, etc.
or even stock market indices.
Options
An option is another type of derivative instrument regularly traded in the
derivatives segment of stock exchanges or in separate futures and options
exchanges. One type of options contract, the call option, gives the investor
the right to buy an underlying asset at a predetermined price at a certain time
in the future. The investor will exercise the right if the future price movement
is favourable to him; or else he will choose not to exercise the right. Another
type of options contract, the put option, gives the holder of the option the
right to sell the underlying asset at a predetermined price in the future.
Investors can use options contracts to protect themselves against adverse
movements in the future prices of the underlying assets such as shares,
foreign currencies, stock market indices, etc.
Investment in securities is a rewarding exercise; but it is also a risky exercise.
Persons engaged in such activities need to understand the nature and
functions of securities markets and also the trading system in such markets.
Analysis of securities has to be carried out seriously and in a professional
style so as to identify fundamentally strong securities and to select the
appropriate timing of investment. Investment in an optimal combination of
securities is necessary to minimize the risk in investment. Periodic revision
and final evaluation of the investment portfolio are sequels to the
construction of an optimal portfolio. Security analysis and portfolio
management have to be combined with trading in derivative instruments so as
to hedge the risk involved in financial investment. An understanding of
securities market, security analysis, portfolio management and derivative
trading is thus essential for profitable investment in securities.
REVIEW QUESTIONS
1. What is a portfolio?
2. What is portfolio management?
3. Describe the different phases in portfolio management.
4. Compare and contrast briefly fundamental analysis and technical
analysis.
5. What is portfolio revision? Why is it necessary?
6. “Portfolio evaluation provides a feedback mechanism for improving the
entire portfolio management process.” Explain.
7. Trace the evolution of investment management over the years,
highlighting the important developments.
8. What is the status of portfolio management in India?
REFERENCES
1. Myer, John N., 1978, Financial Statement Analysis, 4th ed., pp. 6−7,
Prentice-Hall of India, New Delhi.
2. Francis, J.C., 1986, Investments: Analysis and Management, 4th ed., pp.
1−2, McGraw-Hill, New York.
INVESTMENT
The income that a person receives may be used for purchasing goods and
services that he currently requires or it may be saved for purchasing goods
and services that he may require in the future. In other words, income can be
what is spent for current consumption or saved for the future consumption.
Savings are generated when a person or an organisation abstains from present
consumption for a future use. The person saving a part of his income tries to
find a temporary repository for his savings until they are required to finance
his future expenditure. This results in investment.
MEANING OF INVESTMENT
Investment is an activity that is engaged in by people who have savings, i.e.
investments are made from savings, or in other words, people invest their
savings. But all savers are not investors. Investment is an activity which is
different from saving. Let us see what is meant by investment.
It may mean many things to many persons. If one person has advanced some
money to another, he may consider his loan as an investment. He expects to
get back the money along with interest at a future date. Another person may
have purchased one kilogram of gold for the purpose of price appreciation
and may consider it as an investment. Yet another person may purchase an
insurance plan for the various benefits it promises in future. That is his
investment.
In all these cases it can be seen that investment involves employment of
funds with the aim of achieving additional income or growth in values. The
essential quality of an investment is that it involves waiting for a reward.
Investment involves the commitment of resources which have been saved in
the hope that some benefits will accrue in future.
Thus, investment may be defined as “a commitment of funds made in the
expectation of some positive rate of return”1. Expectation of return is an
essential element of investment. Since the return is expected to be realised in
future, there is a possibility that the return actually realised is lower than the
return expected to be realised. This possibility of variation in the actual return
is known as investment risk. Thus, every investment involves return and risk.
FINANCIAL
AND
INVESTMENT
ECONOMIC
MEANING
OF
In the financial sense, investment is the commitment of a person’s funds to
derive future income in the form of interest, dividend, premiums, pension
benefits or appreciation in the value of their capital. Purchasing of shares,
debentures, post office savings certificates, insurance policies are all
investments in the financial sense. Such investments generate financial assets.
In the economic sense, investment means the net additions to the economy’s
capital stock which consists of goods and services that are used in the
production of other goods and services. Investment in this sense implies the
formation of new and productive capital in the form of new constructions,
plant and machinery, inventories, etc. Such investments generate physical
assets.
The two types of investments are, however, related and dependent. The
money invested in financial investments are ultimately converted into
physical assets. Thus, all investments result in the acquisition of some assets
either financial or physical.
CHARACTERISTICS OF INVESTMENT
All investments are characterised by certain features. Let us analyse these
characteristic features of investments.
Return
All investments are characterised by the expectation of a return. In fact,
investments are made with the primary objective of deriving a return. The
return may be received in the form of yield plus capital appreciation. The
difference between the sale price and the purchase price is capital
appreciation. The dividend or interest received from the investment is the
yield. Different types of investments promise different rates of return. The
return from an investment depends upon the nature of the investment, the
maturity period and a host of other factors.
Risk
Risk is inherent in any investment. This risk may relate to loss of capital,
delay in repayment of capital, non-payment of interest, or variability of
returns. While some investments like government securities and bank
deposits are almost riskless, others are more risky. The risk of an investment
depends on the following factors.
1. The longer the maturity period, the larger is the risk.
2. The lower the credit worthiness of the borrower, the higher is the risk.
3. The risk varies with the nature of investment. Investments in ownership
securities like equity shares carry higher risk compared to investments in
debt instruments like debentures and bonds.
Risk and return of an investment are related. Normally, the higher the risk,
the higher is the return.
Safety
The safety of an investment implies the certainty of return of capital without
loss of money or time. Safety is another feature which an investor desires for
his investments. Every investor expects to get back his capital on maturity
without loss and without delay.
Liquidity
An investment which is easily saleable or marketable without loss of money
and without loss of time is said to possess liquidity. Some investments like
company deposits, bank deposits, P.O. Deposits, NSC, NSS, etc. are not
marketable. Some investment instruments like preference shares and
debentures are marketable, but there are no buyers in many cases and hence
their liquidity is negligible. Equity shares of companies listed on stock
exchanges are easily marketable through the stock exchanges.
An investor generally prefers liquidity for his investments, safety of his
funds, a good return with minimum risk or minimisation of risk and
maximisation of return.
OBJECTIVES OF INVESTMENT
An investor has various alternative avenues of investment for his savings to
flow to. Savings kept as cash are barren and do not earn anything. Hence,
savings are invested in assets depending on their risk and return
characteristics. The objective of the investor is to minimise the risk involved
in investment and maximise the return from the investment.
Our savings kept as cash are not only barren because they do not earn
anything, but also loses its value to the extent of rise in prices. Thus, rise in
prices or inflation erodes the value of money. Savings are invested to provide
a hedge or protection against inflation. If the investment cannot earn as much
as the rise in prices, the real rate of return would be negative. Thus, if
inflation is at an average annual rate of ten per cent, then the return from an
investment should be above ten per cent to induce savings to flow into
investment.
Thus, the objectives of an investor can be stated as:
1. Maximisation of return
2. Minimisation of risk
3. Hedge against inflation.
Investors, in general, desire to earn as large returns as possible with the
minimum of risk. Risk here may be understood as the probability that actual
returns realised from an investment may be different from the expected
return. If we consider the financial assets available for investment, we can
classify them into different risk categories. Government securities would
constitute the low risk category as they are practically risk free. Debentures
and preference shares of companies may be classified as medium risk assets.
Equity shares of companies would form the high risk category of financial
assets. An investor would be prepared to assume higher risk only if he
expects to get proportionately higher returns. There is a trade-off between
risk and return. The expected return of an investment is directly proportional
to its risk. Thus, in the financial market, there are different financial assets
with varying risk-return combinations.
The investors in the financial market have different attitudes towards risk and
varying levels of risk bearing capacity. Some investors are risk averse, while
some may have an affinity to risk. The risk bearing capacity of an investor,
on the other hand, is a function of his income. A person with higher income is
assumed to have a higher risk bearing capacity. Each investor tries to
maximise his welfare by choosing the optimum combination of risk and
expected return in accordance with his preference and capacity.
INVESTMENT vs SPECULATION
Investment and speculation are two terms which are closely related. Both
involve purchase of assets like shares and securities. Traditionally,
investment is distinguished from speculation with respect to three factors,
viz. (1) risk, (2) capital gain and (3) time period.
Risk
It refers to the possibility of incurring a loss in a financial transaction. It
arises from the possibility of variation in returns from an investment. Risk is
invariably related to return. Higher return is associated with higher risk.
No investment is completely risk free. An investor generally commits his
funds to low risk investment, whereas a speculator commits his funds to
higher risk investments. A speculator is prepared to take higher risks in order
to achieve higher returns.
Capital Gain
The speculator’s motive is to achieve profits through price changes, i.e. he is
interested in capital gains rather than the income from the investment. If
purchase of securities is preceded by proper investigation and analysis to
receive a stable return and capital appreciation over a period of time, it is
investment. Thus, speculation is associated with buying low and selling high
with the hope of making large capital gains. A speculator consequently
engages in frequent buying and selling transactions.
Time Period
Investment is long-term in nature, whereas speculation is short-term. An
investor commits his funds for a longer period and waits for his return. But a
speculator is interested in short-term trade gains through buying and selling
of investment instruments.
Analysis of these distinctions helps us to identify the role of an investor and a
speculator. An investor is interested in a good rate of return earned on a
rather consistent basis for a relatively longer period of time. He evaluates the
worth of a security before investing in it. A speculator seeks opportunities
promising very large returns earned rather quickly. He is interested in market
action and price movements. Consequently, speculation is more risky than
investment.
Basically, both investment and speculation aim at good returns. The
difference is in motives and methods. As a result, the distinction between
investment and speculation is not very wide. Investment is sometimes
described as ‘a well grounded and carefully planned speculation’.
INVESTMENT vs GAMBLING
Investment has also to be distinguished from gambling. Typical examples of
gambling are horse races, card games, lotteries, etc. Gambling consists in
taking high risks not only for high returns, but also for thrill and excitement.
Gambling is unplanned and non scientific, without knowledge of the nature
of the risk involved. It is surrounded by uncertainty and is based on tips and
rumours. In gambling artificial and unnecessary risks are created for
increasing the returns.
Investment is an attempt to carefully plan, evaluate and allocate funds to
various investment outlets which offer safety of principal and moderate and
continuous return over a long period of time. Gambling is quite the opposite
of investment.
TYPES OF INVESTORS
Investors may be individuals and institutions. Individual investors operate
alongside institutional investors in the investment arena. However, their
characteristics are different.
Individual investors are large in number but their investable resources are
comparatively smaller. They generally lack the skill to carry out extensive
evaluation and analysis before investing. Moreover, they do not have the time
and resources to engage in such an analysis.
Institutional investors, on the other hand, are the organisations with surplus
funds who engage in investment activities. Mutual funds, investment
companies, banking and non-banking companies, insurance corporations, etc.
are the organisations with large amounts of surplus funds to be invested in
various profitable avenues. These institutional investors are fewer in number
compared to individual investors, but their investable resources are much
larger. The institutional investors engage professional fund managers to carry
out extensive analysis and evaluation of different investment opportunities.
As a result their investment activity tends to be more rational and scientific.
They have a better chance of maximising returns and minimising risk.
The professional investors and the unskilled individual investors combine to
make the investment arena dynamic.
INVESTMENT AVENUES
There are a large number of investment avenues for savers in India. Some of
them are marketable and liquid while others are non marketable. Some of
them are highly risky while some others are almost riskless. The investor has
to choose proper avenues from among them depending on his preferences,
needs and ability to assume risk.
The investment avenues can be broadly categorised under the following
heads:
1. Corporate securities
2. Deposits in banks and non-banking companies
3. UTI and other mutual fund schemes
4. Post office deposits and certificates
5. Life insurance policies
6. Provident fund schemes
7. Government and semi-government securities.
Let us discuss briefly the important investment avenues available to savers in
India.
Corporate Securities
Corporate securities are the securities issued by joint stock companies in the
private sector. These include equity shares, preference shares and debentures.
Equity shares have variable dividend and hence belong to the high risk—high
return category, while preference shares and debentures have fixed returns
with lower risk.
Deposits
Among the non-corporate investments, the most popular are deposits with
banks such as savings accounts and fixed deposits. Savings deposits have low
interest rates whereas fixed deposits have higher interest rates varying with
the period of maturity. Interest is payable quarterly or half-yearly. Fixed
deposits may also be recurring deposits wherein savings are deposited at
regular intervals. Some banks have reinvestment plans wherein the interest is
reinvested as it gets accrued. The principal and accumulated interest are paid
on maturity.
Joint stock companies also accept fixed deposits from the public. The
maturity period varies from three to five years. Fixed deposits in companies
have high risk since they are unsecured, but they promise higher returns than
bank deposits.
Fixed deposit in non-banking financial companies (NBFCs) is another
investment avenue open to savers. NBFCs include leasing companies, hire
purchase companies, investment companies, chit funds, etc. Deposits in
NBFCs carry higher returns with higher risk compared to bank deposits.
UTI and other Mutual Fund Schemes
Mutual funds offer various investment schemes to investors. UTI is the oldest
and the largest mutual fund in the country. Unit Scheme 1964, Unit Linked
Insurance Plan 1971, Master Share, Master Equity Plans, Mastergain, etc. are
some of the popular schemes of UTI. A number of commercial banks and
financial institutions have set up mutual funds. Recently mutual funds have
been set up in the private sector also.
Post Office Deposits and Certificates
The investment avenues provided by post offices are generally nonmarketable. Moreover, the major investments in post office enjoy tax
concessions also. Post offices accept savings deposits as well as fixed
deposits from the public. There is also a recurring deposit scheme which is an
instrument of regular monthly savings.
Six-year National Savings Certificates (NSC) are issued by post offices to
investors. The interest on the amount invested is compounded half-yearly and
is payable along with the principal at the time of maturity which is six years
from the date of issue.
Indira Vikas Patra and Kissan Vikas Patra are savings certificates issued by
post offices.
Life Insurance Policies
The Life Insurance Corporation (LIC) offers many investment schemes to
investors. These schemes have the additional facility of life insurance cover.
Some of the schemes of LIC are Whole Life Policies, Convertible Whole Life
Assurance Policies, Endowment Assurance Policies, Jeevan Saathi, Money
Back Plan, Jeevan Dhara, Marriage Endowment Plan, etc.
Provident Fund Schemes
Provident fund schemes are compulsory deposit schemes applicable to
employees in the public and private sectors. There are three kinds of
provident funds applicable to different sectors of employment, namely
Statutory Provident Fund, Recognised Provident Fund and Unrecognised
Provident Fund.
In addition to these, there is a voluntary provident fund scheme which is open
to any investor whether employed or not. This is known as the Public
Provident Fund (PPF). Any member of the public can join the scheme
which is operated by the post offices and the State Bank of India.
Government and Semi-Government Securities
The government and semi-government bodies like the public sector
undertakings borrow money from the public through the issue of government
securities and public sector bonds. These are less risky avenues of investment
because of the credibility of the government and government undertakings.
Let us now summarise the discussion on investment.
SUMMARY
Investment is a financial activity that involves risk. It is the commitment of
funds for a return expected to be realised in the future. Investments may be
made in financial assets or physical assets. In either case there is the
possibility that the actual return may vary from the expected return. That
possibility is the risk involved in investment.
Risk and return are two important characteristics of any investment. Safety
and liquidity are also important for an investor. The objective of an investor
is specified as maximisation of return and minimisation of risk.
Investment is generally distinguished from speculation in terms of three
factors, namely risk, capital gains and time period. Gambling is the extreme
form of speculation. Investors may be individuals or institutions. Both type of
investors combine to make investment activity dynamic and profitable.
There are a large number of investment avenues for savers in India.
Corporate securities, deposits in banks and non-banking companies, mutual
fund schemes, provident fund schemes, life insurance policies, government
securities are some of the important investment avenues.
REVIEW QUESTIONS
1. Define investment.
2. Distinguish between the financial and economic meaning of investment.
3. What are the characteristics that an investor would like to have in an
investment option? Explain each of these characteristics.
4. State and explain the objectives of investment activity.
5. “There is a trade-off between risk and return.” Explain this statement.
6. Distinguish between investment and speculation.
7. “Investment is well-grounded and carefully planned speculation.”
Discuss.
8. Describe the features that distinguish institutional investors from
individual investors.
9. Describe briefly the important investment avenues available to savers in
India.
REFERENCE
1. Fischer, Donald E. and Ronald J. Jordan, 1994, Security Analysis and
Portfolio Management, 5th ed., p. 2, Prentice-Hall of India, New Delhi.
SECURITIES MARKET
Corporate securities and government securities constitute important
investment avenues for savers. These are traded in the securities market.
Creation of a portfolio and periodic revision of the portfolio involves buying
and selling of securities in the securities market. An understanding of the
working of securities market is, therefore, essential for practising portfolio
management. However, the functioning of the securities market is too vast a
subject to be confined within a single chapter. An attempt is made in this
chapter to explain the basic features of securities market.
FINANCIAL MARKET
A market is a place used for buying and selling goods. This is the
commonest meaning of the word ‘market’. The usual features of a market are
a place, some buyers, some sellers, some commodity to be exchanged for
money or some other commodity. What transpires in a market is an exchange
of a commodity between a buyer and a seller. However, such an exchange
can take place even without a common meeting place or physical space.
Hence, a physical place is not an essential constituent of a market. It is rather
the mechanism used for the exchange of goods.
In an ordinary market what is usually exchanged is a physical commodity
such as fruits, grains, etc. In modern day markets, these commodities are
valued in monetary terms and exchanged for money. A commodity that is in
demand is exchanged between buyers and sellers in the market.
In an economy, the various economic units such as individuals in the
household sector, business units in the industrial and commercial sector, and
government organisations and departments in the government sector are
engaged in various economic activities and transactions involving money.
Some of them spend more money than they earn and end up in financial
deficit while others earn more money than they spend, thus ending up in
financial surplus. The deficit generators are usually the units in the industrial,
commercial and government sectors. The surplus generators are mostly the
units in the household sector. The deficit generators who are known as
ultimate borrowers would like to borrow funds from the surplus generators
who are the primary lenders. Such transfer of funds is possible and also
necessary to sustain the development of the economy.
The transfer of funds between primary lenders and ultimate borrowers takes
place through the creation of securities or financial assets. If an individual is
not spending all his income on consumption, he will want to find a temporary
repository for his current savings until they are required to finance future
consumption. This involves the purchase of a financial asset or security. If
the investor deposits the money in the fixed deposit of a commercial bank,
the bank issues him a fixed deposit receipt which is a financial asset. The
individual is purchasing a financial asset and thereby transferring the surplus
funds at his disposal to a financial intermediary. The bank, in turn, may lend
the money to a business unit through the creation of a loan agreement.
Let us consider another instance of transfer of funds. A company in need of
funds may issue shares to mobilise funds. In a public issue of shares, any
individual with surplus funds may participate. If shares are allotted to such an
individual, the company which is the borrower of funds will issue a share
certificate to the investor who is the lender of funds. In such a situation a
financial asset in the form of a share certificate is being exchanged. This
exchange represents a marketing transaction and presupposes a market which
nevertheless has no physical location. The commodity being exchanged is a
financial asset instead of a physical asset. The lender of funds (or investor) is
the buyer of the asset and the borrower of funds is the seller of the asset (or
issuer of the security). The mechanism or system through which financial
assets are created and transferred is known as the financial market. When
the financial assets transferred are corporate securities and government
securities, the mechanism of transfer is known as securities market.
Segments of Financial Market
Different types of securities are traded in the securities market. These may
include ownership securities, debt securities, short-term securities, long-term
securities, government securities, non-government or corporate securities.
The nature of return and risk involved in short-term securities is vastly
different from that of long-term securities. Hence, on the basis of the maturity
period of securities traded in the market, the securities market is segmented
into money market and capital market. Money market is the market for shortterm financial assets with maturities of one year or less. Treasury bills,
commercial bills, commercial paper, certificate of deposit, etc. are the shortterm securities traded in the money market. These instruments being close
substitutes for money, the market for their trading is known as money market.
Money market is the main source of working capital funds for business and
industry. It provides a mechanism for evening out short-term surpluses and
deficits. The short-term requirements of borrowers can be met by the creation
of money market securities, which can be purchased by lenders with shortterm surpluses to park their funds for short durations. In India, the money
market has a narrow base with limited number of participants who are mostly
financial institutions.
Capital market, on the other hand, is the market segment where securities
with maturities of more than one year are bought and sold. Equity shares,
preference shares, debentures and bonds are the long-term securities traded in
the capital market. The capital market is the source of long-term funds for
business and industry.
Types of Financial Market
The financial market may be classified as primary market or secondary
market depending on whether the securities traded are newly issued securities
or securities already outstanding and owned by investors. Private companies
and public sector enterprises, in need of money, may issue securities such as
shares, debentures, bonds, commercial papers, etc. to raise required capital.
Individual investors and institutional investors may invest in these securities.
The market mechanism for the buying and selling of new issues of securities
is known as primary market. This market is also termed as new issues
market because it deals in new issues of securities.
The secondary market, on the other hand, deals with securities which have
already been issued and are owned by investors, both individual and
institutional. These may be traded between investors. The buying and selling
of securities already issued and outstanding take place in stock exchanges.
Hence, stock exchanges constitute the secondary market in securities.
Participants in the Financial Market
A financial market is essentially a system by which financial securities are
exchanged. This system is composed of participants, securities, markets,
trading arrangements and regulations. The major participants are the buyers
and sellers of securities or the investors (who are the buyers of securities) and
the issuers (who are the sellers of securities). Financial intermediaries are the
second major class of participants in the financial system. They play a crucial
role in the smooth functioning of the financial system. The investors who are
the primary lenders in the financial system would prefer to ‘lend short’, that
is, invest their surplus for short durations as they generally have a preference
for liquidity. On the contrary, the issuers of securities who are the ultimate
borrowers would prefer to ‘borrow long’, that is, borrow for long durations as
the funds are generally required for financing long-term investment in fixed
assets. This situation gives rise to a fundamental problem in the financial
system which was described as the ‘constitutional weakness’ of
unintermediated financial markets by Hicks (1939).1 The problem is to match
the preferences of the surplus sector to lend short with those of the deficit
sector to borrow long. It is the financial intermediaries who resolve this
problem. They borrow for short durations from the primary lenders and lend
for long durations to the ultimate borrowers. Through the intervention of the
financial intermediaries, the ultimate borrower is able to get long-term
funding and the primary lender is able to get liquidity on his lending.
There are two types of financial intermediaries in the financial system,
namely banking financial intermediaries and non-banking financial
intermediaries such as insurance companies, housing finance companies, unit
trusts and investment companies. However, it may be noted that the
traditional distinction between banking and non-banking institutions is slowly
disappearing. As a result of technological innovations and increasing
competitive pressures, the traditional distinction between banking and nonbanking activities is rapidly disappearing and a universal banking system in
which a single institution provides the complete range of financial
intermediation services is slowly emerging.
Another group of participants in the financial system comprises the
individuals and institutions who facilitate the trading or exchange process in
the system. They are primarily brokers who act as agents for the primary
lenders or the ultimate borrowers in the purchase or sale of securities. There
are also broker dealers who act on their own account by buying and selling
securities for a profit. This group also includes institutions which act as
registrars, managers, lead managers, share transfer agents, etc. at the time of
issue of shares by companies.
Regulatory Environment
The financial system in a country is subject to a set of regulations in the form
of various Acts passed by the legislative bodies. The regulatory environment
may differ from one country to another. In each country, the regulatory
control of the financial system is exercised by designated regulatory
authorities. In India, the Ministry of Finance, the Reserve Bank of India
(RBI), the Securities and Exchange Board of India (SEBI), etc. are the major
regulatory bodies exercising regulatory control and supervision over the
functioning of the financial system in the country.
A simple diagrammatic representation of how a security is raised or
originated in the financial market is attempted in Fig. 3.1.
The securities thus issued may be traded or exchanged between investors in
securities markets with the help of intermediaries, within the regulatory
framework approved by the Government and other regulatory bodies.
New securities are directly issued by the issuing companies to the investors.
All the participants in this process of issuing new shares to investors together
constitute the primary market or new issues market. Let us analyse the
functioning of this primary market.
PRIMARY MARKET/NEW ISSUES MARKET
When a new company is floated, its shares are issued to the public in the
primary market as an Initial Public Offer (IPO). If the company subsequently
decides to include debt in its capital structure by issuing bonds or debentures,
these may also be floated in the primary market. Similarly, when a company
decides to expand its activities using either equity finance or bond finance,
the additional shares or bonds may be floated in the primary market.
The primary market or new issues market (NIM) does not have a physical
structure or form. All the agencies which provide the facilities and participate
in the process of selling new issues to the investors constitute the NIM.
The NIM has three functions to perform. They are:
1. Origination
2. Underwriting
3. Distribution.
Origination
Origination is the preliminary work in connection with the floatation of a new
issue by a company. It deals with assessing the feasibility of the project,
technical, economic and financial, as also making all arrangements for the
actual floatation of the issue. As part of the origination work, decisions may
have to be taken on the following issues:
1. Time of floating the issue
2. Type of issue
3. Price of the issue.
Timing of the issue is crucial for its success. The floatation of the issue
should coincide with the buoyant mood in the investment market to ensure
proper support and subscription to the issue. The type of issue whether
equity, preference, debentures or convertible securities, has to be properly
analysed at the time of origination work. Pricing of the issue is a sensitive
matter, as the public support to a new issue will depend on the price of the
issue to a large extent. In the primary market, the price of the security is
determined by the issuer and not by the market. New issues are made either at
par or at premium. Well-established companies may be able to sell their
shares at a premium at the time of a new issue. Further, the pricing of new
issues is also regulated by the guidelines on capital issues issued by SEBI.
The origination function in the NIM is now being carried out by merchant
bankers. In the 1980s, commercial banks in India created special divisions
called merchant banking divisions to perform the origination function for
floatation of new issues. But now there are separate institutions registered
with SEBI as merchant bankers.
Underwriting
The second function performed by NIM is underwriting which is the activity
of providing a guarantee to the issuer to ensure successful marketing of the
issue. An underwriter is an individual or institution which gives an
undertaking to the stock issuing company to purchase a specified number of
shares of the company in the event of a shortfall in subscription to the new
issue. The stock issuing company can thus ensure full subscription to the new
issue through underwriting agreements with different underwriters, even if
there is no proper response to the new issue from the investors. Underwriting
activity in the NIM is performed by large financial institutions such as LIC,
UTI, IDBI, IFCI, general insurance companies, commercial banks and also
by brokers. The underwriters earn commission from the issuing company for
this activity.
Distribution
The new issue market performs a third function besides the functions of
origination and underwriting. This third function is that of distribution of
shares. The distribution function is carried out by brokers, sub-brokers and
agents. New issues have to be publicised by using different mass media, such
as newspapers, magazines, television, radio, Internet, etc. New issues are also
publicised by mass mailing. It has become a general practice to distribute
prospectus, application forms and other literature regarding new issues
among the investing public.
Methods of Floating New Issues
The methods by which new issues of shares are floated in the primary market
in India are:
1. Public issue
2. Rights issue
3. Private placement.
Public Issue
Public issue involves sale of securities to members of the public. The issuing
company makes an offer for sale to the public directly of a fixed number of
shares at a specific price. The offer is made through a legal document called
Prospectus. Thus a public issue is an invitation by a company to the public to
subscribe to the securities offered through a prospectus. Public issues are
mostly underwritten by strong public financial institutions. This is the most
popular method for floating securities in the new issue market, but it involves
an elaborate process and consequently it is an expensive method. The
company has to incur expenses on various activities such as advertisements,
printing of prospectus, banks’ commissions, underwriting commissions,
agents’ fees, legal charges, etc.
Rights Issue
The rights issue involves selling of securities to the existing shareholders in
proportion to their current holding. As per section 81 of the Companies Act,
1956, when a company issues additional equity capital it has to be offered
first to the existing shareholders on a pro rata basis. However, the
shareholders may forfeit this special right by passing a special resolution and
thereby enable the company to issue additional capital to the public through a
public issue. Rights issue is an inexpensive method of floatation of shares as
the offer is made through a formal letter to the existing shareholders.
Private Placement
A private placement is a sale of securities privately by a company to a
selected group of investors. The securities are normally placed, in a private
placement, with the institutional investors, mutual funds or other financial
institutions. The terms of the issue are negotiated between the company and
the investors. A formal prospectus is not necessary in the case of private
placement. Underwriting arrangements are also not required in private
placement, as the sale is directly negotiated with the investors. This method is
useful to small companies and closely held companies for issue of new
securities, because such companies are unlikely to get good response from
the investing public for their public issues. They can avoid the expenses of a
public issue and also have their shares sold.
Principal Steps in Floating a Public Issue
In a public issue, investors are allowed to subscribe to the shares being issued
by the company during a specified period ranging from a minimum of three
days to a maximum of ten days. The issue remains open during this period for
subscription by the public. This is the principal activity in the process of a
public issue. Before the issue is opened for public subscription, several
activities/legal formalities have to be completed. These are the pre-issue steps
or obligations. Similarly, after the issue is closed, several activities are to be
carried out to complete the process of public issue. These activities may be
designated as the post-issue tasks. Thus, we can identify three distinct stages
in the successful completion of a public issue.
1. Pre-issue tasks
2. Opening and closing of the issue
3. Post-issue tasks.
Pre-issue Tasks
These are the preparatory obligations to be complied with before the actual
opening of the issue.
Drafting and finalisation of the prospectus Prospectus is an essential
document in a public issue. The Companies Act 1956 defines a prospectus as:
“Any document described or issued as a prospectus and includes any notice,
circular, advertisement or other document inviting deposits from the public or
inviting offers from the public for the subscription or purchase of any shares
in or debentures of a body corporate”. It is the offer document which contains
all the information pertaining to the company which will be useful to the
investors to arrive at a proper decision regarding investing in the company. It
is a communication from the issuer to the investor. The prospectus contains
detailed information about the company, its activities, promoters, directors,
group companies, capital structure, terms of the present issue, details of
proposed project, details regarding underwriting arrangements, etc. SEBI has
issued guidelines regarding the contents of the prospectus and these have to
be complied with by the company.
The draft prospectus has to be approved by the Board of Directors of the
company. The draft prospectus has also to be filed with SEBI and the
Registrar of companies. The final prospectus has to be prepared as per the
suggestions of SEBI and filed with SEBI and the Registrar of companies.
Selecting the intermediaries and entering into agreements with them
Several intermediaries are involved in the process of a public issue. These
intermediaries have to be registered with SEBI. Important categories of
intermediaries are the following:
1. Merchant banker: Merchant banker is any person or institution which
is engaged in the business of issue management either as manager,
consultant, adviser, or by rendering corporate advisory service in
relation to such issue management. Merchant bankers play an important
role in the process of managing a public issue. It is the duty of the
merchant bankers to ensure correctness of the information furnished in
the prospectus as well as to ensure compliance with SEBI rules,
regulations and guidelines regarding public issue of securities. Merchant
bankers are registered with SEBI in four categories, with different
eligibility criteria for each category.
2. Registrar to an issue: Registrar to an issue is any person or institution
entrusted with the following functions in connection with a public issue:
(a) Collecting applications from investors.
(b) Keeping a record of applications and monies received from
investors
(c) Assisting the stock issuing company in determining the basis of
allotment of securities in consultation with the stock exchange.
(d) Finalising the list of persons entitled to allotment of securities.
(e) Processing and despatching allotment letters, refund orders,
certificates and other related documents.
3. Share transfer agent: Share transfer agent is a person or institution
which maintains the records of holders of securities of a company on
behalf of that company. The share transfer agent is authorised to effect
the transfer of securities as well as the redemption of securities wherever
applicable.
4. Banker to an issue: Banker to an issue is a scheduled bank entrusted
with the following activities in connection with a public issue:
(a) Acceptance of application and application monies
(b) Acceptance of allotment or call monies
(c) Refund of application monies
(d) Payment of dividend or interest warrants.
The intermediaries are service providers possessing professional expertise in
the relevant areas of operation. The market regulator, SEBI, regulates the
various intermediaries in the primary market through its regulations for these
intermediaries. SEBI has defined the role of each category of intermediary,
the eligibility criteria for granting registration, their functions and
responsibilities, and the code of conduct to which they are bound.
The stock issuing company has to select the intermediaries such as merchant
banker, registrar to the issue, share transfer agent, banker to the issue,
underwriters, etc. and sign separate agreements with each of them to engage
them for the public issue.
Attending to other formalities The prospectus and application forms have
to be printed and despatched to all intermediaries and brokers for wide
circulation among the investing public. An initial listing application has to be
filed with the stock exchange where the issue is proposed to be listed. An
abridged version of the prospectus along with the issue opening and closing
dates has to be published in newspapers.
Opening and closing of the issue The public issue is open for subscription
by the public on the pre-announced opening date. The application forms and
application monies are received at the branches of the bankers to the issue
and forwarded by these bankers to the Registrar to the issue. Two closing
dates are prescribed for the closing of the public issue. The first of these is
the ‘earliest closing date’ which should not be less than three days from the
opening date. If sufficient applications are received by the company, the
company may choose to close the issue on the earliest closing date itself. The
other closing date is the final or latest closing date which shall not exceed ten
days from the opening date.
Post-issue Tasks
After closing of the public issue, several activities are to be carried out to
complete the process of public issue. They are:
1. All the application forms received have to be scrutinised, processed and
tabulated.
2. When the issue is not fully subscribed to, it becomes the liability of the
underwriters to subscribe to the shortfall. The liability of each
underwriter has to be determined.
3. When the issue is oversubscribed, the basis of allotment has to be
decided in consultation with the stock exchange.
4. Allotment letters and share certificates have to be despatched to the
allottees. Refund orders have to be despatched to the applicants whose
applications are rejected.
5. Shares have to be listed in the stock exchange for trading. For this
purpose. the issuing company has to enter into a listing agreement with
the stock exchange.
Book Building
Companies may raise capital in the primary market by way of public issue,
rights issue or private placement. A public issue is the selling of securities to
the public in the primary market. The usual procedure of a public issue is
through the fixed price method where securities are offered for subscription to
the public at a fixed price. An alternative method is now available which is
known as the book building process. Although book building has been a
common practice in most of the developed countries, the concept is relatively
new in India. SEBI announced guidelines for the book building process, for
the first time, in October 1995.
Under the book building process, the issue price is not fixed in advance. It is
determined by the offer of potential investors about the price which they are
willing to pay for the issue. The price of the security is determined as the
weighted average at which the majority of investors are willing to buy the
security. Thus, under the book building process, the issue price of a security
is determined by the demand and supply forces in the capital market.
SEBI guidelines define book building as: “A process undertaken by which a
demand for the securities proposed to be issued by a body corporate is
elicited and built up and the price for such securities is assessed for the
determination of the quantum of such securities to be issued by means of a
notice, circular, advertisement, document or information memoranda or offer
document”.
Book building is a process of price discovery. It puts in place a pricing
mechanism whereby new securities are valued on the basis of the demand
feedback following a period of marketing. It is an alternative to the existing
system of fixed pricing.
A public issue of securities may be made through the fixed price method, the
book building method, or a combination of both. In case the issuing company
chooses to issue securities through the book building route, then as per SEBI
guidelines the issuer company can select any of the following methods:
1. 100 per cent of the offer to the public through the book building process.
2. Seventy-five per cent of the offer to the public through the book building
process and twenty-five per cent through the fixed price method at the
price determined through book building.
3. Ninety per cent of the offer to the public through the book building
process and ten per cent through the fixed price method.
The issue of the fixed price portion is conducted like a normal public issue
after the book built portion is issued.
The steps involved in the process of book building may be listed out as
follows:
1. The issuer appoints a merchant banker as the lead manager and book
runner to the issue.
2. The book runner forms a syndicate of underwriters. The syndicate
consists of book runner, lead manager, joint lead managers, advisors, comanagers and underwriting members.
3. A draft prospectus is submitted to SEBI without a price or price band.
The draft prospectus is then circulated among eligible investors with a
price band arrived at by the book runner in consultation with the issuer.
Such a prospectus is known as a Red Herring prospectus.
4. The book runner conducts awareness campaigns, which include
advertising, road shows and conferences.
5. Investors place their orders with syndicate members. These members
collect orders from their clients on the amount of securities required by
them as well as the price they are willing to pay.
6. The book runner builds up a record known as Book after receiving orders
from members of the syndicate. He maintains detailed records in this
regard. The book is thus built up to the size of the portion to be raised
through the book building process. When the book runner receives
substantial number of orders, he announces closure of the book. A book
should remain open for a minimum of three working days. The
maximum period for which the bidding process may be allowed is seven
working days.
7. On the basis of the offers received, the book runner and the issuer
company then determines the price at which the securities shall be sold.
8. The book runner finalises the allocation to syndicate members.
Procurement agreements are signed between issuer and the syndicate
members for the subscription to be procured by them.
9. The final prospectus along with the procurement agreements is then filed
with the Registrar of companies within two days of the determination of
the offer price.
10. The book runner collects from the institutional buyers and the
underwriters the application forms along with the application monies to
the extent of the securities proposed to be allotted to them/subscribed by
them.
Book building is a process wherein the issuer of securities asks investors to
bid for their securities at different prices. These bids should be within an
indicative price band decided by the issuer. Here investors bid for different
quantity of shares at different prices. Considering these bids, issuer
determines the price at which the securities are to be allotted. Thus, the issuer
gets the best possible price for his securities as perceived by the market or
investors.
Role of Primary Market
Primary market is the medium for raising fresh capital in the form of equity
and debt. It mops up resources from the public (investors) and makes them
available for meeting the long-term capital requirements of corporate
business and industry. The primary market brings together the two principal
constituents of the market, namely the investors and the seekers of capital.
The savings or surplus funds with the investors are converted into productive
capital to be used by companies for productive purposes. Thus, capital
formation takes place in the primary market. The economic growth of a
country is possible only through a robust and vibrant primary market.
In the secondary market, shares already purchased by investors are traded
among other investors. Operations in the secondary market do not result in
the accretion of capital resources of the country, but indirectly promotes
savings and investments by providing liquidity to the investments in
securities, i.e. the investors have the facility to liquidate their investments in
securities in the secondary market.
Regulation of Primary Market
For companies, raising capital through the primary market is time consuming
and expensive. The issuer has to engage the services of a number of
intermediaries and comply with complex legal and other formalities. The
investor faces much risk while operating in the primary market. Fraudulent
promoters may try to dupe the investors who opt to invest in a new issue.
Investors in the primary market need protection from such fraudulent
operators.
Up to 1992, the primary market was controlled by the Controller of Capital
Issues (CCI) appointed under the Capital Issues Control Act, 1947. During
that period, the pricing of capital issues was regulated by CCI. The Securities
and Exchange Board of India (SEBI) was formed under the SEBI Act, 1992,
with the prime objective of protecting the interests of investors in securities
as well as for promoting and regulating the securities market. All public
issues since January 1992 are governed by the rules, regulations and
guidelines issued by SEBI.
SEBI has been instrumental in bringing greater transparency in capital issues.
It has issued detailed guidelines to standardise disclosure obligations of
companies issuing securities. Companies floating pubic issues are now
required to disclose all relevant information affecting investors’ interests.
SEBI constantly reviews its guidelines to make them more market friendly
and investor friendly.
Successful floatation of a new issue in the primary market requires careful
planning, proper timing and comprehensive marketing efforts. The services
of specialised institutions such as merchant bankers, registrars to the issue,
underwriters, etc. are available to the issuer company to handle the task.
There is effective regulation of SEBI at every stage of a public issue. There
are also regulations to ensure fair practice by the intermediaries in the market.
REVIEW QUESTIONS
1. What is a financial market?
2. Distinguish between money market and capital market.
3. Who are the participants in the financial market? Describe their role.
4. Explain how a financial security/asset is created in the financial market.
5. What is meant by new issue market?
6. Describe the functions of NIM.
7. Write short notes on:
(a) Underwriting
(b) Private placement
(c) Prospectus
(d) Merchant banker
8. Distinguish between public issue and rights issue.
9. Describe the principal steps in floating a public issue.
10. Explain the functions of market intermediaries in a public issue.
11. List out pre-issue and post-issue tasks.
12. What is book building?
13. “Book building is a process of price discovery.” Discuss.
14. Explain the steps involved in a book building process.
15. “Capital formation takes place in the primary market.” Explain.
16. What is the role of SEBI in regulating the new issue market/primary
market.
REFERENCE
1. Blake, David, 1992, Financial Market Analysis, p. 4, McGraw-Hill,
London.
STOCK EXCHANGES
Primary market is the market in which new issues of securities are sold by the
issuing companies directly to the investors. Secondary market is the market
in which securities already issued by companies are subsequently traded
among investors. A person with funds for investment in securities may
purchase the securities either in the primary market (from the issuing
company at the time of a new issue of securities) or from the secondary
market (from other investors holding the desired securities). Securities can be
purchased in the primary market only at the time of issue of the security by
the company, whereas in the secondary market securities can be purchased
throughout the year. As a result, trading in a particular security in the primary
market is an intermittent event depending upon the frequency of new issues
of the security by the company, but trading in that security in the secondary
market is continuous. The secondary market where continuous trading in
securities takes place is the stock exchange. In this chapter we shall examine
the functioning of stock exchanges in the country.
WHAT IS A STOCK EXCHANGE
The stock exchanges were once physical market places where the agents of
buyers and sellers operated through the auction process. These are being
replaced with electronic exchanges where buyers and sellers are connected
only by computers over a telecommunications network. Auction trading is
giving way to “screen-based” trading, where bid prices and offer prices (or
ask prices) are displayed on the computer screen. Bid price refers to the price
at which an investor is willing to buy the security and offer price refers to the
price at which an investor is willing to sell the security. Alternatively, a
dealer in securities may declare the bid price and the offer price of a security,
suggesting the price at which he is prepared to buy the security (bid price)
and also the price at which he is prepared to sell the security (offer price).
The bid-offer spread, the difference between the bid price and the offer price
constitutes his margin or profit.
Securities of a company first become available on an exchange after the
company conducts its Initial Public Offering (IPO). During the IPO, a
company sells it securities to
an initial set of investors in the primary market. These securities can then be
sold and purchased in the stock exchanges. The exchange tracks the flow of
orders for each security, and this flow of supply and demand for the security
sets the price of the security.
A stock exchange may be defined or described in different ways. A simple
description of a stock exchange is as follows: “A centralised market for
buying and selling stocks where the price is determined through supplydemand mechanisms”.
A somewhat similar description of a stock exchange is the following: “An
organisation that provides a facility for buyers and sellers of listed securities
to come together to make trades in these securities”.
In a stock exchange, the trading in listed securities is carried out by qualified
members who may act either as agents for customers or as principals for their
own accounts. Stock exchanges may, therefore, be described as "Associations
of brokers and dealers in securities who transact business together”.
A more descriptive definition of a stock exchange is: “An organised market
place for securities featured by the centralisation of supply and demand for
the transaction of orders by member brokers for institutional and individual
investors”.
According to the Securities Contracts (Regulation) Act, 1956, which is the
main law governing stock exchanges in India, “stock exchange means any
body of individuals, whether incorporated or not, constituted for the purpose
of assisting, regulating or controlling the business of buying, selling or
dealing in securities”.
Functions of Stock Exchanges
A stock exchange has an important role to fulfil in the economic development
of a country. It is essential for the smooth functioning of the private sector
corporate economy. In the process of capital formation and in raising
resources for the corporate sector, the stock exchange performs four essential
functions.
Firstly, it provides a market place for purchase and sale of securities such as
shares, bonds, debentures, etc. Investors desirous of buying securities would
be able to buy securities in the primary market only occasionally, that is, at
the time of issue of such securities by the company, whereas they would be
able to buy securities in the stock exchanges at any time, as trading in stock
exchanges is continuous. Similarly, holders of securities who are desirous of
selling the securities would be able to sell them only in the stock exchanges,
as the issuing companies do not ordinarily buy back the shares. Thus, stock
exchanges provide the facility for continuous trading in securities.
Secondly, stock exchanges provide liquidity to the investments in securities,
that is, it gives the investors a place to liquidate their holdings. This is
essentially the basis for the joint stock enterprise system. Investors would not
be interested to invest in corporate securities without the assurance provided
by the stock exchanges to the owners of corporate securities that these
securities can be sold in the stock exchanges at any time.
Thirdly, the stock exchanges help in the valuation of securities by providing
the market quotations of the prices of securities. The market quotations
represent the collective judgement on the value of the securities arrived at
simultaneously by many sellers and buyers in the market. The value of shares
is influenced by macro economic factors as well as micro economic factors,
long-term economic trends as well as short-term fluctuations in economic
variables. Speculative forces in the securities market also influence share
valuations. Market quotations of share prices provide valuable information to
prospective investors as well as shareholders regarding the value of shares
traded in the stock exchanges.
Fourthly, stock exchanges play the role of a barometer, namely, an indicator
of the state of health of the nation’s economy as a whole. The shares of a
large number of companies are listed for trading in the important stock
exchanges of the country. The market quotations of individual shares
represent their current valuation. The trend of price movements in the market
is indicated by calculating stock market indices which represent the weighted
average of prices of selected shares representing all the important industries.
These stock market indices are used to represent the share market as a whole.
Their movements and levels are indicative of the economic health of the
nation to a great extent because movements of prices of shares are influenced
by macro economic factors such as growth of GDP, financial and monetary
policies, tax changes, political environment, etc.
The stock exchanges provide the linkage between the savings in the
household sector and the investments in the corporate sector. They indirectly
help in mobilising savings and channelising them into the corporate sector as
securities.
STOCK MARKET IN INDIA
The Indian securities market has become one of the most dynamic and
efficient securities market in Asia today. The Indian market now conforms to
international standards in terms of operating efficiency. In this context, it
would be informative to understand the origin and growth of the Indian stock
market.
During the latter half of the 19th century, shares of companies used to be
floated in India occasionally. There were share brokers in Bombay who
assisted in the floatation of shares of companies. A small group of stock
brokers in Bombay joined together in 1875 to form an association called
Native Share and Stockbrokers Association. The association drew up
codes of conduct for brokerage business and mobilised private funds for
investment in the corporate sector. It was this association which later became
the Bombay Stock Exchange, which is the oldest stock exchange in Asia.
This exchange is now known as The Stock Exchange, Mumbai, or BSE.
Ahmedabad was a major centre of cotton textile industry. After 1880, many
new cotton textile mills were started in and around Ahmedabad. As new
cotton textile enterprises were floated, the need for a stock exchange at
Ahmedabad was strongly felt. Accordingly, in 1894, the brokers of
Ahmedabad formed The Ahmedabad Share and Stockbrokers Association,
which later became the Ahmedabad Stock Exchange, the second stock
exchange of the country.
During the 1900s Kolkata became another major centre of share trading on
account of the starting of several indigenous industrial enterprises. As a
result, the third stock exchange of the country was started by the Kolkata
stockbrokers at Kolkata in 1908. As industrial activity in the country gained
momentum, existing enterprises in cotton textiles, woollen textiles, tea, sugar,
paper, steel, engineering goods, etc. began to undertake expansion activities
and new ventures were also floated. Yet another stock exchange was started
in 1920 at Chennai. However, by 1923, it ceased to exist. Later, in 1937, the
Madras Stock Exchange was revived as many new cotton textile mills and
plantation companies were floated in South India. Three more stock
exchanges were established before independence, at Indore in Madhya
Pradesh in 1930, at Hyderabad in 1943 and at Delhi in 1947. Thus, at the
time of independence, seven stock exchanges were functioning in the major
cities of the country.
The number of stock exchanges virtually remained unchanged for nearly
three decades from 1947 to 1977, except for the establishment of the
Bangalore Stock Exchange in 1957. During the 1980s, however, many stock
exchanges were established. Some of them were:
1. Cochin Stock Exchange (1978)
2. Uttar Pradesh Stock Exchange (at Kanpur, 1982)
3. Pune Stock Exchange (1982)
4. Ludhiana Stock Exchange (1983)
5. Gauhati Stock Exchange (1984)
6. Kanara Stock Exchange (at Mangalore, 1985)
7. Magadh Stock Exchange (at Patna, 1986)
8. Jaipur Stock Exchange (1989)
9. Bhubaneswar Stock Exchange (1989)
10. Saurashtra Kutch Stock Exchange (at Rajkot, 1989)
11. Vadodara Stock Exchange (at Baroda, 1990).
Thus, from seven stock exchanges in 1947, the number of stock exchanges in
the country increased to eighteen by 1990. Along with the increase in the
number of stock exchanges, the number of listed companies and the capital of
the listed companies has also grown, especially after 1985. Two more stock
exchanges were set up at Coimbatore and Meerut during the 1990s, taking the
total to twenty.
Over the Counter Exchange of India (OTCEI)
The traditional trading mechanism (floor trading using open outcry system),
which prevailed in the Indian stock exchanges, resulted in much functional
inefficiency such as absence of liquidity, lack of transparency, undue delay in
settlement of transactions, fraudulent practices, etc. With the objective of
providing more efficient services to investors, the country’s first electronic
stock exchange which facilitates ringless, scripless trading was set up in 1992
with the name Over the Counter Exchange of India (OTCEI). It was
sponsored by the country’s premier financial institutions such as UTI, ICICI,
IDBI, SBI Capital Markets, IFCI, GIC and its subsidiaries and Canbank
Financial services.
The exchange was set up to aid enterprising promoters in raising finance for
new projects in a cost effective manner and to provide investors with a
transparent and efficient mode of trading. The OTCEI had many novel
features. It introduced screen based trading for the first time in the Indian
stock market. Trading takes place through a network of computers of over the
counter (OTC) dealers located at several places, linked to a central OTC
computer using telecommunication links. All the activities of the OTC
trading process are fully computerised. Moreover, OTCEI is a national
exchange having a country-wide reach. OTCEI has an exclusive listing of
companies, that is, it does not ordinarily list and trade in companies listed in
any other stock exchanges. For being listed in OTCEI the companies have to
be sponsored by members of OTCEI. It was the first exchange in the country
to introduce the practice of market making, that is, dealers in securities
providing two-way quotes (bid prices and offer prices of securities).
National Stock Exchange of India (NSE)
With the liberalisation of the Indian economy during the 1990s, it was
inevitable that the Indian stock market trading system be raised to the level of
international standards. The high powered committee on stock exchanges
known as Pherwani Committee recommended, in 1991, the setting up of a
new stock exchange as a model exchange and to function as a national stock
exchange. It was envisaged that the new exchange should be completely
automated in terms of both trading and settlement procedures. On the basis of
the recommendations of the Pherwani committee, a new stock exchange was
promoted by the premier financial institutions of the country, namely IDBI,
ICICI, IFCI, all insurance corporations, selected commercial banks and
others. The new exchange was incorporated in 1992 as the National Stock
Exchange (NSE). It started functioning in June 1994.
The purpose of setting up the new exchange was to create a world-class
exchange and use it as an instrument of change in the Indian stock market
through competitive pressure. Technology has been the backbone of NSE. It
chose to harness technology in creating a new market design. Its trading
system, called National Exchange for Automated Trading (NEAT), is a stateof-the-art client-server based application. The NSE also uses satellite
communication technology for trading. Its trading system has shifted the
trading platform from the trading hall in the premises of the exchange to the
computer terminals at the premises of the trading members located at
different geographical locations in the country. It has been instrumental in
bringing about many changes in the trading system such as reduction of
settlement cycle, dematerialisation and electronic transfer of securities,
establishment of clearing corporations, professionalisation of trading
members, etc.
All the stock exchanges in the country, starting with the Bombay Stock
Exchange, have shifted to the new computerised trading system which
facilitates screen-based trading. As a consequence, the stock market today
uses the state-of-the-art information technology tools to provide an efficient
and transparent trading, clearing and settlement mechanism at par with
international standards. The National Stock Exchange has played a leading
role as a change agent in transforming the Indian stock market to its present
form. Since its inception, the NSE has been playing the role of a catalytic
agent in reforming the stock market and evolving the best market practices.
The NSE has brought about unparalleled transparency, speed and efficiency,
safety and market integrity. In this process the NSE has become the largest
stock exchange in the country, relegating the Bombay Stock Exchange to the
second place.
Inter-connected Stock Exchange of India (ISE)
With the setting up of the National Stock Exchange in 1994, a transformation
of the Indian stock market was initiated. Automated screen-based trading,
rolling settlement on T + 2 cycle, dematerialisation of securities with
electronic transfer of securities, etc. completely transformed the market
structures and procedures. Gradually, the two national stock exchanges, BSE
and NSE dominated the scene with practically all trading being routed
through either of these exchanges. The regional stock exchanges became
irrelevant as they could not compete with the breadth and depth of these two
stock exchanges, and there was virtually no trading at any of the nineteen
regional centres. The members of the regional stock exchanges of the country
started investing large amounts of money in automating their trading, clearing
and settlement systems on account of regulatory compulsions. This situation
prompted the regional stock exchanges to devise some way of reviving their
fortunes. It was decided to evolve an inter-connected market system by
pooling the resources of the regional stock exchanges. Fourteen regional
stock exchanges (excluding Calcutta, Delhi, Ahmedabad, Ludhiana and Pune
stock exchanges) joined together and promoted a new organisation called
Inter-connected Stock Exchange of India Ltd. (ISE) in 1998. The ISE was
recognised as a stock exchange by SEBI and it commenced trading in
February, 1999. It then began to function as a national level stock exchange.
The objective of setting up ISE was to optimally utilise the existing
infrastructure and other resources of participating stock exchanges which
were until now underutilised. The ISE aims to provide cost-effective trading
linkage/connectivity to all the members of the participating exchanges on a
national level. This will help to widen the market for the securities listed on
the regional stock exchanges. Through ISE an attempt is made to make the
regional markets vibrant and liquid through the use of the state of the art
technology and networking. The trading settlement and funds transfer
operations of the ISE are completely automated. However, ISE has not
succeeded in becoming a competitive market force to BSE and NSE. This is
mainly because the participating regional stock exchanges did not close down
their regional segments.
At present there are twenty-three stock exchanges in the country. Four of
them can be considered as national level exchanges, namely, NSE, BSE,
OTCEI and ISE; the remaining nineteen are regional stock exchanges (RSEs)
located in important cities of the country. But it may be noted that most of the
trading in securities in the country are transacted through the two largest
stock exchanges, namely the National Stock Exchange (NSE) and the Stock
Exchange, Mumbai (BSE) which have trading terminals all over the country.
Even in these exchanges, even though there are a large number of companies
listed, active daily trading takes place only in the securities of a limited
number of companies. The large volume of trading is accounted for by
limited number of securities. For the vast majority of securities of listed
companies, the stock exchanges fail to provide liquidity.
MCX-SX: The newest stock exchange of the country
MCX Stock Exchange Ltd (MCX-SX) is the newest stock exchange to be set
up in India. It is projected as India’s third national stock exchange after
Bombay Stock Exchange and National Stock Exchange. MCX-SX has been
co-promoted by MCX (Multi Commodity Exchange), the country’s largest
commodity exchange, and FTIL (Financial Technologies India Ltd), both
enterprises promoted by Jignesh Shah. The shareholders of MCX-SX include
India’s top public sector banks, private sector banks and domestic financial
institutions. The new exchange started with trading in currency futures in
2008.
The important milestones in its growth to a full-fledged stock exchange are
listed below:
Commenced operations in the Currency Derivatives segment on
October 7, 2008.
Notified as a ‘recognized stock exchange’ by Government of India,
after approval by SEBI, on December 21, 2012.
Launched Capital Market segment, Futures and Options segment on
February 9, 2013 and commenced trading in these segments from
February 11, 2013.
Launched the flagship index of the exchange ‘SX40’ on February 9,
2013 and commenced trading in ‘SX40’ index derivatives from
May 15, 2013.
Launched Debt Market segment on June 7, 2013 and commenced
trading from June 10, 2013.
Commenced trading in Interest Rate Futures (IRF) on 10-year GOI
security from January 20, 2014.
The new exchange, MCX-SX, follows global best practices in its operations.
Clearing and settlement of trades in the exchange is done through a separate
clearing corporation — MCX-SX Clearing Corporation Ltd. MCX-SX has to
function in direct competition with NSE, India’s biggest stock exchange by
volumes and turnover, and BSE, India’s oldest stock exchange.
SX40—The market index of MCX-SX
‘SX40’ is the flagship index of MCX-SX, similar to Sensex (including 30
shares) of BSE and Nifty (including 50 shares) of NSE. SX40 includes 40
large cap liquid stocks representing diverse sectors of the economy. Only
companies that have a minimum free float (shares that are readily available
for trading) of 10 percent and are within the top 100 liquid companies are
included in SX40. Companies are selected for inclusion in the index on the
basis of free float weighted market capitalization. The base value of SX40 is
10,000 and the base date is March 31, 2010.
ORGANISATION, MEMBERSHIP AND MANAGEMENT
OF STOCK EXCHANGES
Basically, a stock exchange is an organised market for trading securities. It is
also called a bourse. It is an association or organisation of individuals which
is governed by certain rules and regulations. The manner of organisation and
the rules of membership are important features of stock exchanges as also the
governance system of the organisation.
Over the years, stock exchanges in the country have been organised in
various forms such as voluntary non-profit making association, public limited
company and company limited by guarantee. In India, the earliest stock
exchanges were organised as voluntary non-profit making associations of
persons. Later on, stock exchanges began to be organised as companies.
The membership of stock exchanges initially comprised of individuals and
partnership firms. It was the stock brokers who became members of stock
exchanges either in their individual capacity or by forming partnership firms.
Later on companies were also allowed to become members of stock
exchanges. Thus, stock exchanges now have both individual and institutional
membership. Membership in stock exchanges is restricted and limited. It is
acquired by paying the prescribed entrance fee/share value. Members are also
supposed to make security deposit and pay annual subscription to the
exchange. The quantum of entrance fee/share value, security deposit and
annual subscription vary from exchange to exchange.
The management of each stock exchange is vested in a Governing Board
which is the apex body deciding the policies of the exchange as also
regulating the affairs of the exchange. The composition of the governing
board is of a heterogeneous nature. It usually consists of elected directors
(mostly from the broking community), SEBI nominees and public
representatives. The governing board is usually presided over by an executive
director or president. The executive director/president as the Chief Executive
Officer (CEO) of the exchange is responsible for the day-to-day
administration of the exchange. The governing board may constitute
executive committees of its members to supervise and monitor specific
functions.
The BSE governing board has twenty members consisting of nine elected
directors, three SEBI nominees, six public representatives, an executive
director (CEO), and a non- executive chairman. The governing board of the
National Stock Exchange comprises senior executives from promoter
institutions, eminent professionals in the fields of law, economics,
accountancy, finance, taxation, etc., public representatives, nominees of SEBI
and one full-time executive of the exchange.
The governing board of an exchange has wide powers for the management
and administration of the stock exchange concerned. These powers include
wide ranging discretionary powers also. The important powers of the
governing body are:
1. Manage and control the functioning of the exchange.
2. Regulate trading in securities.
3. Admit, fine, suspend or expel members and take such disciplinary action
as it deems fit.
4. Settle disputes, if any, amongst the members and between members and
non-members.
5. Make or amend any rules, by-laws or regulations or suspend their
operations with the approval of the government.
6. Interpret the rules, by-laws and regulations.
The stock exchanges have to comply with the directions of the SEBI.
LISTING OF SECURITIES
For the securities of a company to be traded on a stock exchange, they have
to be listed in that stock exchange. Listing is the process of including the
securities of a company in the official list of the stock exchange for the
purpose of trading.
At the time of issue of securities, a company has to apply for listing the
securities in a recognised stock exchange. The Securities Contracts
Regulation Act and rules, SEBI guidelines, and the rules and regulations of
the exchange prescribe the statutory requirements to be fulfilled by a
company for getting its shares listed in a stock exchange. Important
documents such as memorandum of association, articles of association,
prospectus, directors’ report, annual accounts, agreement with underwriters,
etc. and detailed information about the company’s activities, its capital
structure, distribution of shares, dividends and bonus shares issued, etc. have
to be submitted to the stock exchange along with the application for listing.
The stock exchange examines whether the company satisfies the criteria
prescribed for listing. When the stock exchange finds that a company is
eligible for listing its securities at the exchange, the company would be
required to execute a listing agreement with the stock exchange. This listing
agreement contains the obligations and restrictions imposed on the company
as a result of listing. The company is also required to pay the annual listing
fees every year.
The purpose of the listing agreement is to compel the company to keep the
shareholders and investors informed about the various activities which are
likely to affect the share prices of the company. A company whose securities
are listed in a stock exchange is obliged to keep the stock exchange fully
informed about all matters affecting the company. Moreover, the company
has to forward copies of its audited annual accounts to the stock exchange as
soon as they are issued.
The securities of companies listed on a stock exchange may be classified into
different groups. For instance, the securities listed on the Bombay Stock
Exchange (BSE) have been classified into A, B1, B2, F, G and Z groups. The
equity shares listed in the exchange have been grouped under three groups,
namely A, B1 and B2, based on certain qualitative and quantitative
parameters which include number of trades, value traded, etc. The F group
represents the fixed income securities. The G group includes Government
securities for retail investors. The Z group includes companies which have
failed to comply with the listing requirements of the exchange or have failed
to resolve investor complaints or have not made arrangements with the
depositories for dematerialisation of their securities.
Permitted Securities
The securities of companies which have signed listing agreement with an
exchange are traded at the exchange as listed securities. A stock exchange
sometimes permits trading in certain securities which are not listed at the
exchange but are actively traded in other stock exchanges. Such securities are
known as permitted securities. This facility is provided to help market
participants to trade in certain actively traded securities even though they are
not formally listed at the exchange. Thus, a stock exchange may have certain
listed securities and certain permitted securities, and trading may take place
in these securities regularly.
REGULATION OF STOCK EXCHANGES
The stock exchanges play a very vital and sensitive role in the functioning of
the economy, especially the private sector of the economy. The functioning
of the exchanges, therefore, needs to be transparent, fair and efficient. This is
ensured through proper regulation of the working of stock exchanges. There
are Acts, rules, regulations, by-laws and guidelines governing the functioning
of secondary markets or stock exchanges in the country. There is also a
regulator in the form of the Securities and Exchange Board of India (SEBI) to
oversee and monitor the functioning of both the primary and secondary
securities markets in India.
The Securities Contracts (Regulation) Act, 1956, and the rules made under
the Act, namely the Securities Contracts (Regulation) Rules, 1957, constitute
the main laws governing stock exchanges in India. The preamble to the Act
states that it is “an act to prevent undesirable transactions in securities by
regulating the business of dealing therein”. This Act provides for the direct
and indirect control of virtually all aspects of securities trading and the
functioning of stock exchanges.
The provisions of the Securities Contracts (Regulation) Act, 1956, were
formerly administered by the Central Government. However, since the
enactment of the Securities and Exchange Board of India Act, 1992, the
Board established under this Act has been authorised to administer almost all
the provisions of the Securities Contracts (Regulation) Act. The various
provisions of the Act deal with recognition of stock exchanges, submission of
relevant documents, approval of by-laws and rules made by stock exchanges,
listing of securities in stock exchanges and such other matters relating to the
trading of securities and the functioning of stock exchanges.
Taking into consideration the fact that the securities market in India had
shown tremendous growth, the government decided to set up a separate board
for the regulation and orderly functioning of the securities market in the
country, in the model of the Securities and Investment Board (SIB) of UK
and the Securities and Exchange Commission (SEC) of USA.
Initially, the Securities and Exchange Board of India was constituted as an
interim administrative body in 1988. SEBI was given a statutory status on
30th January 1992 by an ordinance to provide for the establishment of SEBI.
Later, in April 1992, the Securities and Exchange Board of India Act was
passed. In this Act it is stipulated that it shall be the duty of the Board to
protect the interests of investors in the securities market and to promote the
development of and to regulate the securities market.
Thus, the SEBI has been constituted to promote orderly and healthy
development of the securities market and to ensure adequate protection to the
investors in the securities market. The Board plays a dual role, namely a
regulatory role and a developmental role.
The SEBI is constituted with six members, including the chairman of the
Board. Two members are officials of the central government ministries of
Finance and Law, one member is an official of the Reserve Bank of India and
two members are professionals having experience or special knowledge
relating to securities markets and are appointed by the central government.
The Board is empowered to regulate the business in stock exchanges, to
register and regulate the working of stock market intermediaries such as stock
brokers, sub-brokers, share transfer agents, bankers to an issue, trustees of
trust deeds, registrars to an issue, merchant bankers, underwriters, etc. The
Board is also authorised to prevent and prohibit fraudulent and unfair trade
practices in the market. It makes regulations and issues guidelines regarding
the various aspects of the working of stock exchanges, and constantly
monitors the activities in the securities market to ensure just and fair dealings.
Transparency and equal opportunity to all market participants have been the
goals of all developmental and regulatory activities of SEBI.
A stock exchange has the power to make by-laws for the regulation and
control of contracts entered into by members and also for the regulation of
trading in the exchange. However, these by-laws have to be approved by
SEBI before implementation. Amendments to the by-laws should also be
similarly approved.
The Depositories Act, 1996, is another important legislation affecting the
functioning of stock exchanges. This Act provides for the setting up of
depositories for electronic recording and transfer of securities. The paperbased securities and their transfer often resulted in delay in the settlement and
transfer of securities and also led to bad delivery, theft, forgery, etc. The
Depositories Act, 1996, was passed to change over to the electronic mode of
security transfer through security depositories so as to improve the efficiency
of the system.
The securities market in India is properly regulated to ensure that it functions
efficiently and effectively. There are strict laws governing the functioning of
stock exchanges; there is a vigilant regulator who oversees the
implementation of these laws. As a result, investors now have confidence in
the efficiency and robustness of the Indian stock market.
REVIEW QUESTIONS
1. What is a stock exchange?
2. How is a stock exchange defined under the Securities Contracts
(Regulation) Act?
3. Describe the functions of stock exchanges.
4. “Stock exchanges act as barometers of the health of the economy.”
Discuss.
5. “Stock exchanges provide the linkage between the savings in the
household sector and the investments in the corporate sector.” Explain.
6. Trace the growth and development of the stock market in India.
7. Write short notes on:
(a) OTCEI
(b) NSE
(c) ISE
(d) Depositories Act, 1996
8. Discuss the role of the NSE in reforming the stock market in India.
9. Describe the current status of stock exchanges in the country.
10. Describe the governance system in stock exchanges.
11. What is meant by listing of securities?
12. What is listing agreement? What is its significance?
13. What are permitted securities?
14. How are stock exchanges in India regulated?
15. What is SEBI? What is its role in the securities market?
TRADING SYSTEM IN STOCK
EXCHANGES
A stock exchange is a market for trading in securities. But it is not an
ordinary market; it is a market with several peculiar features. In a stock
exchange, buyers and sellers do not directly meet and interact with each other
for making their trades. The investors (buyers and sellers of securities) trade
through brokers who are members of a stock exchange. In stock exchanges,
trading procedures are fully automated and member brokers interact and trade
through a networked computer system. Trading in a stock exchange takes
place in two phases; in the first phase, the member brokers execute their buy
or sell orders on behalf of their clients (or investors) and, in the second phase,
the securities and cash are exchanged. For the exchange of securities and cash
between the traders, the services of two other agencies are required, namely
the clearing house (corporation) of the stock exchange and the depositories.
Further, unlike other ordinary markets, stock exchanges are markets where
the prices of the items traded (namely, securities) fluctuate constantly. This
fluctuation in security prices leads to speculative activities in the stock
exchanges.
We need to understand clearly the trading system in stock exchanges, how
the trades are settled through exchange of securities and cash, the role of the
clearing corporation and the depositories, etc. We also need to understand the
different types of speculative activities taking place in a stock exchange. The
information about the prices of securities traded in a stock exchange is useful
in understanding the behaviour of the stock markets.
TRADING SYSTEM
The system of trading prevailing in stock exchanges for many years was
known as floor trading. In this system, trading took place through an open
outcry system on the trading floor or ring of the exchange during official
trading hours.
In floor trading, buyers and sellers transact business face to face using a
variety of signals. Under this system, an investor desirous of buying a
security gets in touch with a broker and places a buy order along with the
money to buy the security. Similarly, an investor intending to sell a security
gets in touch with a broker, places a sell order and hands over the share
certificate to be sold. After the completion of a transaction at the trading floor
between the brokers acting on behalf of the investors, the buyer investor
would receive the share certificate and the seller investor would receive the
cash through their respective brokers.
In the new electronic stock exchanges, which have a fully automated
computerised mode of trading, floor trading is replaced with a new system of
trading known as screen-based trading. In this new system, the trading ring
is replaced by the computer screen and distant participants can trade with
each other through the computer network. The member brokers can install
trading terminals at any place in the country. A large number of participants,
geographically separated from each other, can trade simultaneously at high
speeds from their respective locations. The screen-based trading systems are
of two types:
1. Quote driven system
2. Order driven system.
Under the quote driven system, the market-maker, who is the dealer in a
particular security, inputs two-way quotes into the system, that is, his bid
price (buying price) and offer price (selling price). The market participants
then place their orders based on the bid-offer quotes. These are then
automatically matched by the system according to certain rules.
Under the order driven system, clients place their buy and sell orders with
the brokers. These are then fed into the system. The buy and sell orders are
automatically matched by the system according to predetermined rules.
Types of Orders
An investor can have his buy or sell orders executed either at the best price
prevailing on the exchange or at a price that he determines. Accordingly, an
investor may place two types of orders, namely, market order or limit order.
Market Orders
In a market order, the broker is instructed by the investor to buy or sell a
stated number of shares immediately at the best prevailing price in the
market. In the case of a buy order, the best price is the lowest price
obtainable; in the case of a sell order, it is the highest price obtainable. When
placing a market order, the investor can be fairly certain that the order will be
executed, but he will be uncertain of the price until after the order is
executed.
Limit Orders
While placing a limit order, the investor specifies in advance the limit price at
which he wants the transaction to be carried out. In the case of a limit order to
buy, the investor specifies the maximum price that he will pay for the share;
the order has to be executed only at the limit price or a lower price. In the
case of a limit order to sell shares, the investor specifies the minimum price
he will accept for the share and hence, the order has to be executed only at
the limit price or a price higher to it. Thus for limit orders to purchase shares
the investor specifies a ceiling on the price, and for limit orders to sell shares
the investor specifies a floor price.
Limit orders are generally placed “away from the market” which means that
the limit price is somewhat removed from the prevailing market price. In the
case of a limit order to buy, the limit price would be below the prevailing
price and in the case of a limit order to sell, the limit price would be above
the prevailing market price. The investor placing limit orders believes that his
limit price will be reached and the order executed within a reasonable period
of time. But the limit order may remain unexecuted.
There are certain special types of orders which may be used by investors to
protect their profits or limit their losses. Two such special kinds of orders are
stop orders (also known as stop loss orders) and stop limit orders.
Stop Orders
A stop order may be used by an investor to protect a profit or limit a loss. For
a stop order, the investor must specify what is known as a stop price. If it is a
sell order, the stop price must be below the market price prevailing at the
time the order is placed. If it is a buy order, the stop price must be above the
market price prevailing at the time of placing the order. If, subsequently, the
market price reaches or passes the stop price, the stop order will be executed
at the best available price. Thus, a stop order can be viewed as a conditional
market order, because it becomes a market order when the market price
reaches or passes the stop price.
Examples will help to clarify the working of stop orders. Suppose an investor
has 100 shares of a company which were purchased at ` 35 per share. The
current market price of the share is ` 75. The investor thus has earned a profit
of ` 40 per share on his share holdings. He would very much like to protect
this profit without foregoing the opportunity of earning more profit if the
price moves still upwards. This can be achieved by placing a stop sell order at
a price below the current market price of ` 75, for example at ` 70. Now, if
the price subsequently falls to ` 70 or below, the stop sell order becomes a
market order and it will be executed at the best price prevailing in the market.
Thus, the investor will be able to protect the profit of around ` 35 per share.
On the contrary, if the market price of the share moves upwards, the stop sell
order will not be executed and the investor retains the opportunity of earning
higher profits on his holding.
Stop orders can also be used to minimise loss in trading. Suppose that a share
is currently selling for ` 125 and an investor expects a fall in the price of the
share. He may place an order for sale of the share at the current market price
of ` 125 hoping to cover up his position by purchasing the share at a lower
price and thus make a profit on the deal. This type of a transaction is known
as a short sale. If price of the share falls as anticipated by the investor, he
would make a profit. There is a possibility that the price may move upwards
and in that case the investor has to purchase the share at a higher price to
cover up his position and meet his sales commitment. This will result in a
loss to the investor. This loss can be minimised by placing a stop buy order at
a price above the current price of ` 125, for example at ` 130. Now, if the
price of the share rises to ` 130 or above, the stop buy order will become a
market order and will be executed at the best price available in the market.
Suppose that the stop buy order was executed at ` 131, then the loss of the
investor is limited to ` 6 per share, that is, the difference between the selling
price of ` 125 and the buying price of ` 131 per share.
One disadvantage of the stop orders is that the actual price at which the order
is executed is uncertain and may be some distance away from the stop price.
Stop Limit Orders
The stop limit order is a special type of order designed to overcome the
uncertainty of the execution price associated with a stop order. The stop limit
order gives the investor the opportunity of specifying a limit price for
executing the stop orders: the maximum price for a stop buy order and the
minimum price for a stop sell order. With a stop limit order, the investor
specifies two prices, a stop price and a limit price. When the market price
reaches or passes the stop price, the stop limit order becomes a limit order to
be executed within the limit price. Hence, a stop limit order can be viewed as
a conditional limit order.
Let us consider two examples. Consider a share that is currently selling at `
60. An investor who holds the share may place a stop limit order to sell with
stop price of ` 55 and limit price of ` 52. If the market price declines to ` 55
or lower, a limit order to sell the share at the limit price of ` 52 or higher
would be activated. Here the order will be executed only if the share is
available at ` 52 or above. Thus a stop limit order may remain unexecuted.
Consider an investor who desires to make a short sale of a particular share at
its current market price of ` 85. That is, he intends to sell the share without
owning it but hoping to buy it later from the market at a lower price. He may
also place a stop limit order to buy the share to minimise his loss in case the
share price moves upwards contrary to his expectations. He may specify a
stop price of ` 90 and a limit price of ` 93 for his stop limit order to buy. If the
price moves up to ` 90 or above, then a limit order to buy the share with limit
price of ` 93 would be activated. The order would be executed at a price of `
93 or lower, if such price is available in the market.
The disadvantage of a stop limit order is that it may remain unexecuted. The
stop order results in certain execution at an uncertain price, while a stop limit
order results in uncertain execution within a specified price limit.
Trading in stock exchanges takes place continuously during the official
trading hours. Stock exchanges are open five days a week, from Monday
through Friday. An investor may place orders for trade through his broker at
any time during the official trading hours, but he needs to specify the time
limit for the validity of the order. The time limit on an order is essentially an
instruction to the broker about the time within which he should attempt to
execute the order.
Day Orders
A day order is an order that is valid only for the trading day on which the
order is placed. If the order is not executed by the end of the day, it is treated
as cancelled. All orders are ordinarily treated as day orders unless specified
as other types of orders.
Week Orders
These are orders that are valid till the end of the week during which the
orders are placed. They expire at the close of the trading session on Friday of
the week, unless they are executed by then.
Month Orders
These are orders that are valid till the end of the month during which the
orders are placed. Month orders expire at the close of the trading session on
the last working day of the month.
Open Orders
Open orders are orders that remain valid till they are executed by the brokers
or specifically cancelled by the investor. They are also known as good till
cancelled orders or GTC orders. However, brokers generally seek periodic
confirmation of open orders from the investors.
Fill or Kill Orders
These orders are also known as FoK orders. These orders are meant to be
executed immediately. If not executed immediately, they are to be treated as
cancelled.
SETTLEMENT
Trading in stock exchanges is carried out in two phases. In the first phase, the
execution of the orders submitted by clients takes place between brokers
acting on behalf of the clients or investors. Buy orders are matched with sell
orders. In the automated system, trading is carried out in an anonymous
environment and the orders are matched by the computer system.
The buyer now has to hand over the money and receive the security; the
seller on the other hand has to hand over the security and receive money on
account of the sale of the security. This process of transfer of security and
cash is done in the second phase which is known as the settlement of the
trade. The settlement process involving delivery of securities and payment of
cash is carried out through a separate agency known as the clearing house
which functions in each stock exchange. The clearing house acts as the
counter party for each trade. Member-brokers who sell securities have to
deliver the securities to the clearing house and will receive cash from the
clearing house. Similarly, the member-brokers who buy securities will have
to pay cash to the clearing house and receive the securities from the clearing
house. The stock exchanges now follow a settlement procedure known as
Compulsory Rolling Settlement (CRS) as mandated by SEBI. The earlier
procedure of settlement was “account period settlement” wherein all trades
carried out or executed during an account period of a week or fortnight were
settled on the last day of the account period. The account period used to vary
from exchange to exchange.
Under the rolling settlement system, the trades executed on a particular day
are settled after a specified number of business days or working days.
Initially, a T + 5 settlement cycle was introduced, which was subsequently
reduced to a T + 3 cycle. Currently, a T + 2 settlement cycle is adopted by the
stock exchanges. This means that the settlement of transactions done on T,
that is, the trade day, has to be done on the second business day after the
trade day. The pay-in and pay-out of funds and securities has to take place on
the second business day after the day of trade. For example, for an order
executed on Tuesday of a week, the settlement (delivery of security and
payment of cash) has to be done on Thursday. The pay-in and pay-out of
funds and securities are marked through the clearing house.
On the first business day (T + 1) after the trade day (T), the exchange
generates delivery and receive orders for transactions done by memberbrokers. These provide the relevant information regarding the securities to be
delivered/received by the member- brokers through the clearing house.
Similarly, a money statement showing the details of payments/receipts of
monies by the member-brokers is also prepared by the exchange. The
Delivery/Receive orders and the Money Statement can be downloaded by the
member-brokers.
On the second business day (T + 2) after the day of trade, the memberbrokers are required to submit the pay-in instructions to the depositories for
transfer of securities to the clearing house in the case of demat securities. In
the case of securities in physical form, the certificates have to be delivered to
the clearing house. For pay-in of funds by member-brokers, the bank
accounts of member-brokers maintained with the authorised clearing banks
are directly debited through the computerised system.
For pay-out of securities by the stock exchange, the member-brokers are
required to collect them from the clearing house on the pay-out day, in case
of physical securities. The clearing house arranges for crediting the securities
to the demat accounts of member-brokers, in the case of demat securities.
There is a facility for direct transfer of securities to the investors’ accounts
also. For pay-out of funds by the stock exchange, the bank accounts of
member-brokers with the authorised clearing banks are credited by the
clearing house. In the rolling settlement system, pay-in and pay-out of both
funds and securities are completed on the same day.
The member-brokers are required to make payment to clients for securities
sold and deliver securities purchased by clients within one working day. This
is the time frame permitted to member-brokers to settle their obligations with
the clients as per the by-laws of the exchange.
SPECULATION
People who buy and sell securities in the stock exchanges may have different
motivations for doing so. A person may be interested in getting a good rate of
return, earned on a rather consistent basis, for a relatively long period of time.
For this he will choose the shares of a company which is fundamentally
strong and has the potential for growth in the future. Such a person is a
genuine investor who invests his money in securities for long-term returns.
There may be other persons who have a short-term perspective on their
trading activities on the stock exchanges. A person may be interested in
making a quick short-term profit from the fluctuations in the prices of
securities in the stock market. Such a person is known as a speculator.
Speculators are traders who intend to make high returns within a short span
of time, making use of the short-term fluctuations in security prices.
Speculators constantly monitor the movement of share prices in the market.
On the basis of their analysis of share price movements and on the basis of
the evaluation of various information regarding the performance of
companies, the speculative traders speculate on the future course of prices.
They believe that mispricing of securities occurs periodically in the market.
Sometimes, some securities may be overpriced (that is, their price may be
higher than their intrinsic value) and at other times some securities may be
underpriced. Speculators attempt to exploit such mispricing of securities,
because it is presumed that the mispricing would be corrected by the market
eventually.
Long Buy
If a speculator feels that a security is underpriced or that a security which is
correctly priced at the moment is likely to show a rising trend, then he would
like to buy the security for the purpose of selling it at a higher price when the
price rises as anticipated. The speculator in this case is said to take a long
position with respect to that security. He is not interested in taking delivery
of the security, but intends to sell it off as quickly as possible to gain some
profit. Hence, he would not like to hold his long position for an extended
period. He would like the mispricing to be corrected at the earliest,
preferably, on the same day. Such kind of a speculative activity is known as
long buy.
Short Sale
On the contrary, if a speculator estimates that a security is overpriced and its
price is likely to decline shortly, he would like to sell the security at the
current price and buy it sometime later when the price declines so as to
deliver the security sold at the time of settlement of the trade. Ordinarily, a
person sells securities which he owns. Here, the speculator is selling a
security which he does not own or possess in the hope that he would be able
to deliver the security on the due date by buying it at a lower price within a
short period of time. He hopes to gain some profit in the transaction. The
speculator in this case is taking a “short position” with respect to the security
by engaging in a ‘short sale’. Fundamentally, a short sale is the sale of a
security that is not owned by the seller at the time of the transaction. A short
seller has to cover up his position or eliminate the deficiency by buying the
security sometime in the near future. He will be able to make a profit out of
the short sale transaction only if he is able to buy the security at a lower price.
If the price of a security moves up against his anticipations, he will suffer a
loss.
Speculation involves high amount of risk. The speculators take long or short
positions on the basis of their estimation or speculation about the future
movement of prices. If the prices of securities do not move in the expected
directions within a short time, the speculators suffer losses.
Types of Speculators
Traders engaged in speculative activity in the stock market are described by
different names based on the type of activity they generally engage in. The
prominent among them are bulls, bears, stag and lame duck.
Bull
A trader who expects a rise in prices of securities is known as a bull. He,
therefore, takes a long position with respect to securities. He engages in long
buy anticipating a rise in prices of securities. The bulls will be able to make
profit only if the prices rise as anticipated; otherwise they will suffer losses.
When there is an overbought condition in the market, that is, the purchases
made by speculators exceed the sales made by them; the bulls begin to spread
good rumours about companies so as to raise the price of their shares. This
activity is called a bull campaign.
When the prices of securities are generally rising in the market, resulting in
buoyancy and optimism in the stock market, the market is said to be in a
bullish phase.
Bear
A bear is a pessimist who expects a decline in the prices of securities. He,
therefore, takes a ‘short position’ on securities by engaging in short sales. He
attempts to cover up his short position by buying the securities at lower prices
when prices decline. He may engage in a bear raid so as to bring down the
prices of securities. Spreading unfavourable rumours about companies with
the intention of creating a decline in their share prices is known as a bear
raid. The bear will suffer a loss if the prices of securities rise after he takes a
short position on securities. When there is a general decline in prices of
securities in the stock market, the market is said to be bearish.
Lame Duck
A lame duck is a bear who has made a short sale but is unable to meet his
commitment to deliver the securities sold by him on account of rise in prices
of securities subsequent to the short sale. He is said to be struggling like a
lame duck.
Stag
A stag is a trader who applies for shares in the new issues market just like a
genuine investor. A stag is an optimist like the bull and expects a rise in the
prices of securities that he has applied for. He anticipates that when the new
shares are listed in the stock exchange for trading, they would be quoted at a
premium, that is, above their issue price. As soon as the stag receives the
allotment of shares, he would sell them at the stock exchange at the higher
price and make a profit. A stag is said to be a premium hunter. The stag will,
however, suffer a loss if prices of the new shares do not rise as anticipated
when they are listed for trading.
MARGIN TRADING
Investors may purchase securities in the stock exchanges either using their
own funds or funds borrowed from banks, brokers, etc. Conservative
investors would prefer to use own funds for trading in securities. Other
investors may use borrowed funds for buying securities when there is a good
opportunity to buy some securities but ready cash may not be available.
Borrowing money from the bank or the broker for purchasing securities is
known as margin trading. The investor pays a part of the value of the
securities to be purchased; the balance is provided by the broker or the
banker. The cash paid by the investor is the margin. For example, if an
investor places buy orders for purchase of securities worth ` 50,000 and pays
as cash ` 30,000 to the broker, the investor’s margin is 60 per cent of the
value of the securities. The balance amount is supplied by the broker.
In margin trading, the investor has to pay interest on the money borrowed to
finance the securities transaction. Thus profit or gain from the transaction
would be reduced to that extent. Even if there is no gain from the securities
transaction, interest on the borrowed funds has to be paid. Margin trading is
thus a risky venture.
DEPOSITORIES
Financial securities such as equity shares, bonds and debentures are issued by
companies to the investors who purchase them. They used to be issued in the
form of certificates specifying the name of the holder, the number of
securities comprised in each certificate, the face value of the security, etc.
When the securities are subsequently traded between investors, the seller of
the security hands over the certificate to the buyer through the stock
exchange clearing house. The buyer then forwards the certificate to the
issuing company or its authorised transfer agents to get his name entered in
the certificate as the holder of the security. In this practice, the security has a
physical form, namely that of a paper certificate.
The physical form of securities is giving way to electronic form of securities
wherein a security is represented by an entry in a depository account opened
by the investor for the purpose. The transfer of securities on sale of a security
is effected through a debit entry in the depository account of the seller and a
credit entry in the depository account of the buyer. The securities are issued,
held and transferred in dematerialised form or ‘demat mode’. For the demat
mode of shareholding, depositories play the most important role. Let us
understand what depositories are and how they function.
A depository can be compared to a bank. A bank holds cash for customers
and provides services related to transactions of cash. For this a customer
opens an account in any of the branches of the bank. A depository holds
securities for investors in electronic form and provides services related to
transactions of securities. A depository interacts with clients through
depository participants (DPs) which are organisations affiliated to a
depository. An investor has to open a demat account with a depository
participant to avail depository services of holding securities and transferring
securities. There are two depositories in India namely:
1. National Securities Depository Limited (NSDL)
2. Central Depositories Services (of India) Limited (CDSL)
NSDL was India’s first depository which started functioning on November 6,
1996. CDSL was inaugurated on July 15, 1999. The functioning of these
depositories is supervised and regulated by SEBI. Each depository has
several depository participants affiliated to it.
SEBI has now made it compulsory for trades in almost all listed securities to
be settled in demat mode. For this purpose, registered members of stock
exchanges open clearing member accounts or pool accounts with
depositories. These pool accounts are used by member-brokers to hold
securities from clients and deliver them to the clearing corporation. These
accounts are also similarly used to receive securities from the clearing
corporation for onward distribution to clients.
The demat accounts opened by investors with depository participants are
known as beneficiary accounts. When an investor has sold a security through
a member-broker, he has to deliver the security to the member-broker who, in
turn, has to deliver it to the clearing corporation. The investor has to authorise
his DP to transfer the security from his beneficiary account to the clearing
member’s pool account. Accordingly, the beneficiary account of the investor
would be debited and the pool account of the clearing member would be
credited. The clearing member gives authorisation to his DP to deliver the
securities to the clearing corporation.
When an investor has purchased securities through member-brokers he has to
receive the securities from the member-brokers. In the first instance, the
clearing corporation will instruct its depository to credit the securities to the
pool accounts of member-brokers who are entitled to receive them on pay-out
day. The member-broker then instructs his DP to debit his pool account and
credit the beneficiary account of the client with the securities to be transferred
to the client.
An investor holding securities in the physical form, that is, in the form of
certificates, has the facility to transfer it to the electronic form through the
process of dematerialisation. The process of converting securities held in
physical form (certificates) to an equivalent number of securities in electronic
form and crediting the same to the investor’s demat account is known as
dematerialisation. This is done by the DP on a request from the investor.
Securities in demat form (or electronic form) may again be converted back to
the physical form (certificates), if desired. This process is known as
rematerialisation. At the time of issue of new securities by a company, the
securities allotted to an investor can be directly credited to his demat account.
According to the Depositories Act, 1996, an investor has the option to hold
securities either in physical form or in dematerialised form. But holding
securities in demat form has several advantages. It is safe and also convenient
to hold securities in demat form. Transfer of securities in physical form
involves despatching of certificates through the postal service. This may
result in delay, loss of certificate in transit, theft of certificate, damage to the
certificate, etc. In demat form, transfer of securities is instantaneous and
effortless. Much paper work is done away with in demat mode.
STOCK MARKET QUOTATIONS AND INDICES
In stock exchanges, continuous trading in securities takes place and these
trades occur at different prices. As a result, even on a single day, prices of
securities may fluctuate. On any trading day, four prices can be easily
identified, namely, opening price, closing price, the highest price of the day
and the lowest price of the day. Apart from these short-term intra-day
fluctuations, prices of securities exhibit certain secular trends when
considered over a fairly long period of time. Prices may gradually increase
over a long-term period; or they may decline over the long-term period.
Ordinarily, prices move in a cyclical fashion, alternatively showing
increasing and declining tendencies.
The short-term as well as long-term fluctuations in prices of securities are
indicators of the variations in the underlying economic variables. Hence, it is
necessary to closely observe and monitor the movement of prices in the
securities market. Price information becomes quite valuable for this purpose.
Price quotations of traded securities are available from the stock exchanges
and are being published daily by most of the newspapers. Financial dailies
give very detailed price quotations (opening and closing prices, highest and
lowest prices, 52-week high and low prices, etc.), including the data on
volume of daily trading.
In addition to the price quotations of individual securities, stock exchanges
make available stock market indices, which are useful in understanding the
level of prices and the trend of price movements of the market as a whole.
Stock market indices are meant to capture the overall behaviour of equity
markets.
A stock market index is created by selecting a group of stocks that are
capable of representing the whole market or a specified sector or segment of
the market. The change in the prices of this basket of securities is measured
with reference to a base period. There is usually a provision for giving proper
weights to different stocks on the basis of their importance in the economy. A
stock market index acts as the indicator of the performance of the overall
economy or a sector of the economy.
The Stock Exchange, Mumbai (BSE) came out with a stock index in 1986,
which is known as BSE SENSEX. It is an index composed with 30 stocks
representing a sample of large, well-established and financially sound
companies selected from different industry groups. The base year of BSE
SENSEX is 1978−79 and the base value is 100.
The launch of BSE SENSEX in 1986 was followed up in January 1989 by
another broader index, namely BSE National Index, comprising 100 stocks
listed at five major stock exchanges in India at Mumbai, Kolkata, Delhi,
Ahmedabad and Chennai. The base year of the BSE National Index was
selected as 1983−84, and the base value was taken as 100. This index was
renamed in October 1996 as BSE-100 index and is now calculated by taking
the prices of 100 stocks listed at BSE only.
In 1994, two new index series, namely the BSE-200 and the Dollex-200
indices were launched by BSE. Meanwhile, there has been a steady increase
in the number of listed companies and the market capitalisation of
companies. New industry groups were also emerging. The Stock Exchange,
Mumbai, has been increasing the range of its indices with segment specific
and sector specific indices such as BSE-PSU index to meet the requirements
of market participants for more specific information on the market activities.
The major stock market indices available at the National Stock Exchange
(NSE) are:
1. S and P CNX Nifty
2. CNX Nifty Junior
3. S and P CNX 500
4. CNX Midcap 200
5. S and P CNX Defty.
S and P CNX Nifty
It is an index calculated with a well-diversified sample of fifty stocks
representing 23 sectors of the economy. The base period selected for Nifty is
the close of prices on November 3, 1995, which marks the completion of one
year of operations of NSE’s capital market segment. The base value of the
index has been set at 1000.
Nifty is managed by India Index Services and Products Ltd. (IISL), which is
a joint venture between NSE and CRISIL. The index is known as S and P
index because IISL has consulting and licensing agreement with Standard
and Poor’s (S and P), who are world leaders in index services.
CNX Nifty Junior
It is composed of the next most liquid fifty securities so much so S and P
CNX Nifty and CNX Nifty Junior together account for the hundred most
liquid securities traded at NSE. The two indices are constituted in such a way
as to be disjoint sets, that is, a stock will never appear in both the indices at
the same time.
CNX Midcap 200
It is designed to capture the movement of the mid cap segment or mediumsized capitalisation companies. The medium capitalisation segment of the
stocket market is being perceived increasingly as an attractive investment
segment with high growth potential.
The regional stock exchanges also bring out stock indices calculated from
stocks listed and traded at those exchanges. Many prominent financial dailies
also bring out their own stock market indices.
The price quotations and market index values are useful to investors and
market analysts to understand the mood of the market and to take appropriate
investment decisions.
REVIEW QUESTIONS
1. “A stock exchange is a market with certain peculiar features.” List out
the peculiarities of the stock exchange as a market.
2. What is screen-based trading? How is it different from floor trading?
3. Distinguish between market order and limit order.
4. What is a stop order?
5. Explain how a stop limit order is executed.
6. Distinguish between day order and open order.
7. What is meant by settlement?
8. Explain how a transaction is settled under the rolling system.
9. How are pay-in and pay-out of securities and funds effected ?
10. What is speculation?
11. Write short notes on:
(a) Short sale
(b) Bull
(c) Bear
(d) Stag
(e) BSE Sensex
(f) S and P CNX Nifty
12. What is long buy? When does a speculator take a long position in the
market?
13. Who is a lame duck?
14. What is margin trading?
15. What are depositories? What is a depository participant?
16. Explain the role of depositories in securities trading.
17. “Holding securities in demat form has several advantages.” Discuss.
18. What is a stock market index? How is it calculated?
RISK
Every investment is characterised by return and risk. The concept of risk is
intuitively understood by investors. In general, it refers to the possibility of
incurring a loss in a financial transaction. But risk involves much more than
that. The word ‘risk’ has a definite financial meaning.
MEANING OF RISK
A person making an investment expects to get some return from the
investment in the future. But, as future is uncertain, so is the future expected
return. It is this uncertainty associated with the returns from an investment
that introduces risk into an investment.
We can distinguish between the expected return and the realised return from
an investment. The expected return is the uncertain future return that an
investor expects to get from his investment. The realised return, on the
contrary, is the certain return that an investor has actually obtained from his
investment at the end of the holding period. The investor makes the
investment decision based on the expected return from the investment. The
actual return realised from the investment may not correspond to the expected
return. This possibility of variation of the actual return from the expected
return is termed risk. Where realisations correspond to expectations exactly,
there would be no risk. Risk arises where there is a possibility of variation
between expectations and realisations with regard to an investment.
Thus, risk can be defined in terms of variability of returns. “Risk is the
potential for variability in returns.”1 An investment whose returns are fairly
stable is considered to be a low-risk investment, whereas an investment
whose returns fluctuate significantly is considered to be a high-risk
investment. Equity shares whose returns are likely to fluctuate widely are
considered risky investments. Government securities whose returns are fairly
stable are considered to possess low risk.
ELEMENTS OF RISK
The essence of risk in an investment is the variation in its returns. This
variation in returns is caused by a number of factors. These factors which
produce variations in the returns from an investment constitute the elements
of risk.
Let us consider the risk in holding securities, such as shares, debentures, etc.
The elements of risk may be broadly classified into two groups. The first
group comprises factors that are external to a company and affect a large
number of securities simultaneously. These are mostly uncontrollable in
nature. The second group includes those factors which are internal to
companies and affect only those particular companies. These are controllable
to a great extent. The risk produced by the first group of factors is known as
systematic risk, and that produced by the second group is known as
unsystematic risk.
The total variability in returns of a security represents the total risk of that
security. Systematic risk and unsystematic risk are the two components of
total risk. Thus,
Total risk = Systematic risk + Unsystematic risk
Systematic Risk
As the society is dynamic, changes occur in the economic, political and social
systems constantly. These changes have an influence on the performance of
companies and thereby on their stock prices. But these changes affect all
companies and all securities in varying degrees. For example, economic and
political instability adversely affects all industries and companies. When an
economy moves into recession, corporate profits will shift downwards and
stock prices of most companies may decline. Thus, the impact of economic,
political and social changes is system-wide and that portion of total
variability in security returns caused by such system-wide factors is referred
to as systematic risk. Systematic risk is further subdivided into interest rate
risk, market risk, and purchasing power risk.
Interest Rate Risk
Interest rate risk is a type of systematic risk that particularly affects debt
securities like bonds and debentures. A bond or debenture normally has a
fixed coupon rate of interest. The issuing company pays interest to the bond
holder at this coupon rate. A bond is normally issued with a coupon rate
which is equal to the interest rate prevailing in the market at the time of issue.
Subsequent to the issue, the market interest rate may change but the coupon
rate remains constant till the maturity of the instrument. The change in
market interest rate relative to the coupon rate of a bond causes changes in its
market price.
A bond having a face value of ` 100 issued with a coupon rate of ten per cent
when the market interest rate is also ten per cent will have a market price of `
100. If, subsequent to the issue, the market interest rate moves up to 12.5 per
cent, no investor will buy the bond with ten per cent coupon interest rate
unless the holder of the bond reduces the price to ` 80. When the price is
reduced to ` 80, the purchaser of the bond gets interest of ` ten on an
investment of ` 80 which is equivalent to a return of 12.5 per cent which is
the same as the prevailing market interest rate.
Thus, we see that as the market interest rate moves up in relation to the
coupon interest rate, the market price of the bond declines. Similarly, the
market price of the bond would move up when there is a drop in market
interest rate compared to the coupon rate. In other words, the market price of
bonds and debentures is inversely related to the market interest rates. As a
result, the market price of debt securities fluctuates in response to variations
in the market interest rates. This variation in bond prices caused due to the
variations in interest rates is known as interest rate risk.
The interest rate variations have an indirect impact on stock prices also.
Speculators often resort to margin trading, i.e. purchasing stock on margin
using borrowed funds. As interest rates increase, margin trading becomes less
attractive. The lower demand by speculators may push down stock prices.
The opposite happens when interest rates fall.
Many companies use borrowed funds to finance their operation. When
interest rates move up, companies using borrowed funds have to make higher
interest payments. This leads to lower earnings, dividends and share prices.
On the contrary, lower interest rates may push up earnings and prices. Thus,
we see that variations in interest rates may indirectly influence stock prices.
Interest rate risk is a systematic risk which affects bonds directly and shares
indirectly.
Market Risk
Market risk is a type of systematic risk that affects shares. Market prices of
shares move up or down consistently for some time periods. A general rise in
share prices is referred to as a bullish trend, whereas a general fall in share
prices is referred to as a bearish trend. In other words, the share market
alternates between the bullish phase and the bearish phase. The alternating
movements can be easily seen in the movement of share price indices such as
the BSE Sensitive Index, BSE National Index, NSE Index, etc.
Business cycles are considered to be a major determinant of the timing and
extent of the bull and bear phases of the market. This would suggest that the
ups and downs in share markets would follow the expansion and recession
phase of the economy. This may be true in the long run, but it does not
sufficiently explain the short-term movements in the market.
The short-term volatility in the stock market is caused by sweeping changes
in investor expectations which are the result of investor reactions to certain
tangible as well as intangible events. The basis of the reaction may be a set of
real tangible events, political, economic or social, such as the fall of a
government, drastic change in monetary policy, etc. The change in investor
expectations is usually initiated by the reaction to real events. But the
reaction is often aggravated by the intangible factor of emotional instability
of investors. They tend to act collectively and irrationally, leading to an
overreaction.
The stock market is seen to be volatile. This volatility leads to variations in
the returns of investors in shares. The variation in returns caused by the
volatility of the stock market is referred to as the market risk.
Purchasing Power Risk
Another type of systematic risk is the purchasing power risk. It refers to the
variation in investor returns caused by inflation.
Inflation results in lowering of the purchasing power of money. When an
investor purchases a security, he foregoes the opportunity to buy some goods
or services. In other words, he is postponing his consumption. Meanwhile, if
there is inflation in the economy, the prices of goods and services would
increase and thereby the investor actually experiences a decline in the
purchasing power of his investments and the return from the investment. Let
us consider a simple example. Suppose a person lends ` 100 today at ten per
cent interest. He would get back ` 110 after one year. If during the year, the
prices have increased by eight per cent, ` 110 received at the end of the year
will have a purchasing power of only ` 101.20, i.e. 92 per cent of ` 110. Thus,
inflation causes a variation in the purchasing power of the returns from an
investment. This is known as purchasing power risk and its impact is
uniformly felt on all securities in the market and as such, is a systematic risk.
The two important sources of inflation are rising costs of production and
excess demand for goods and services in relation to their supply. They are
known as cost-push and demand-pull inflation respectively. When demand is
increasing but supply cannot be increased, price of the goods increases
thereby forcing out some of the excess demand and bringing the demand and
supply into equilibrium. This phenomenon is known as demand pull
inflation. Cost push inflation occurs when the cost of production increases
and this increase in cost is passed on to the consumers by the producers
through higher prices of goods.
In an inflationary economy, rational investors would include an allowance for
the purchasing power risk in their estimate of the expected rate of return from
an investment. In other words, the expected rate of return would be adjusted
upwards by the estimated annual rate of inflation.
Unsystematic Risk
The returns from a security may sometimes vary because of certain factors
affecting only the company issuing such security. Examples are raw material
scarcity, labour strike, management inefficiency. When variability of returns
occurs because of such firm—specific factors, it is known as unsystematic
risk. This risk is unique or peculiar to a company or industry and affects it in
addition to the systematic risk affecting all securities.
The unsystematic or unique risk affecting specific securities arises from two
sources: (a) the operating environment of the company, and (b) the financing
pattern adopted by the company. These two types of unsystematic risk are
referred to as business risk and financial risk respectively.
Business Risk
Every company operates within a particular operating environment. This
operating environment comprises both internal environment within the firm
and external environment outside the firm. The impact of these operating
conditions is reflected in the operating costs of the company. The operating
costs can be segregated into fixed costs and variable costs. A larger
proportion of fixed costs is disadvantageous to a company. If the total
revenue of such a company declines due to some reason or the other, there
would be a more than proportionate decline in its operaing profits because it
would be unable to reduce its fixed costs. Such a firm is said to face a larger
business risk.
Business risk is thus a function of the operating conditions faced by a
company and is the variability in operating income caused by the operating
conditions of the company.
Financial Risk
Financial risk is a function of financial leverage which is the use of debt in
the capital structure. The presence of debt in the capital structure creates
fixed payments in the form of interest which is a compulsory payment to be
made whether the company makes profit or loss. This fixed interest payment
creates more variability in the earnings per share (EPS) available to equity
share holders. For example, if the rate of return or operating profit ratio is
higher than the interest rate payable on the debt, EPS would increase. On the
contrary, if the operating profit ratio is lower than the interest rate, EPS
would be depressed. The increase or decrease in EPS in response to changes
in operating profit would be much wider in the case of a levered firm (a
company having debt in its capital structure) than in the case of an unlevered
firm.
This variability in EPS due to the presence of debt in the capital structure of a
company is referred to as financial risk. This is specific to each company and
forms part of its unsystematic risk. Financial risk is an avoidable risk in so far
as a company is free to finance its activities without resorting to debt.
MEASUREMENT OF RISK
An intelligent investor would attempt to anticipate the kind of risk that he is
likely to face. He would also attempt to estimate the extent of risk associated
with different investment proposals. In other words, he tries to measure or
quantify the risk of each investment that he considers before making the final
selection. The quantification of risk is thus necessary for investment analysis.
Risk in investment is associated with return. The risk of an investment cannot
be measured without reference to return. The return, in turn, depends on the
cash inflows to be received from the investment. Let us consider the purchase
of a share. While purchasing an equity share, an investor expects to receive
future dividends declared by the company. In addition, he expects to receive
the selling price when the share is finally sold.
Suppose a share is currently selling at ` 120. An investor who is interested in
the share anticipates that the company will pay a dividend of ` 5 in the next
year. Moreover, he expects to sell the share at ` 175 after one year. The
expected return from this investment can be calculated as follows:
In this case the investor expects to get a return of 50 per cent in the future.
But the future is uncertain. The dividend declared by the company may turn
out to be either more or less than the figure anticipated by the investor.
Similarly, the selling price of the stock may be less than the price anticipated
by the investor at the time of investment. It may sometimes be even more.
Thus, there is a possibility that the future return may be more than 50 per cent
or less than 50 per cent. Since the future is uncertain the investor has to
consider the probability of several other possible returns. The expected
returns may be 30 per cent, 40 per cent, 50 per cent, 60 per cent or 70 per
cent. The investor now has to assign the probability of occurrence of these
possible alternative returns. An example is given below:
Possible returns (in per cent)
Probability of occurrence
Xi
p(Xi)
30
0.10
40
0.30
50
0.40
60
0.10
70
0.10
This table gives the probability distribution of possible returns from an
investment in shares. Such a distribution can be developed by the investor by
studying the past data and modifying it appropriately for the changes he
expects to occur in the future.
The information contained in the probability distribution has to be reduced to
two simple statistical measures in order to aid investment decision-making.
These measures are summary statistics. One measure would indicate the
expected return from the investment and the other measure would indicate the
risk of the investment.
Expected Return
The expected return of the investment is the probability weighted average of
all the possible returns. If the possible returns are denoted by Xi and the
related probabilities are p(Xi), th expected return may be represented as and
can be calculated as:
It is the sum of the products of possible returns with their respective
probabilities.
The expected return of the share in the example given above can be
calculated as follows:
Risk
Expected returns are insufficient for decision-making. The risk aspect should
also be considered. The most popular measure of risk is the variance or
standard deviation of the probability distribution of possible returns.
Variance is usually denoted by σ2 and is calculated by the following formula:
Variance = 116 per cent
Standard deviation is the square root of the variance and is represented as σ.
The standard deviation in our example is
= 10.77 per cent.
The variance and standard deviation measure the extent of variability of
possible returns from the expected return. Several other measures such as
range, semi-variance and mean absolute deviation have been used to measure
risk, but standard deviation has been the most popularly accepted measure.
In the method described above, the probability distribution of possible returns
from an investment proposal is used to estimate the expected return from the
investment and its variability. The mean gives the expected value and the
variance or standard deviation gives the variability. This widely used
procedure for assessing risk is known as the mean-variance approach.
The standard deviation or variance, however, provides a measure of the total
risk associated with a security. Total risk comprises of two components,
namely systematic risk and unsystematic risk. Unsystematic risk is risk which
is specific or unique to a company. Unsystematic risk associated with the
security of a particular company can be reduced by combining it with another
security having opposite characteristics. This process is known as
diversification of investment. As a result of diversification, the investment
is spread over a group of securities with different characteristics. This group
of securities is called a portfolio.
As far as an investor is concerned, the unsystematic risk is not very important
as it can be reduced or eliminated through diversification. It is an irrelevant
risk. The risk that is relevant in investment decision-making is the systematic
risk because it is undiversifiable. Hence, the investor seeks to measure the
systematic risk of a security.
Measurement of Systematic Risk
Systematic risk is the variability in security returns caused by changes in the
economy or the market. All securities are affected by such changes to some
extent, but some securities exhibit greater variability in response to market
changes. Such securities are said to have higher systematic risk. The average
effect of a change in the economy can be represented by the change in the
stock market index. The systematic risk of a security can be measured by
relating that security’s variability with the variability in the stock market
index. A higher variability would indicate higher systematic risk and vice
versa.
The systematic risk of a security is measured by a statistical measure called
Beta. The input data required for the calculation of beta are the historical data
of returns of the individual security as well as the returns of a representative
stock market index. Two statistical methods may be used for the calculation
of Beta, namely the correlation method or the regression method.
Using the correlation method, beta can be calculated from the historical data
of returns by the following formula:
The second method of calculating beta is by using the regression method.
The regression model postulates a linear relationship between a dependent
variable and an independent variable. The model helps to calculate the values
of two constants, namely α and β. β measures the change in the dependent
variable in response to unit change in the independent variable, while α
measures the value of the dependent variable even when the independent
variable has zero value. The form of the regression equation is as follows:
For the calculation of beta, the return of the individual security is taken as the
dependent variable, and the return of the market index is taken as the
independent variable. The regression equation is represented as follows:
Ri = α + βRm
where
Ri = Return of the individual security.
Rm = Return of the market index.
α = Estimated return of the security when the market is stationary.
βi = Change in the return of the individual security in response to unit change
in the return of the market index. It is, thus, the measure of systematic
risk of a security.
A security can have betas that are positive, negative or zero.
“The beta of an asset, βi, is a measure of the variability of that asset relative
to the variability of the market as a whole. Beta is an index of the systematic
risk of an asset.”2
As beta measures the volatility of a security’s returns relative to the market,
the larger the beta, the more volatile the security. A beta of 1.0 indicates a
security of average risk. A stock with beta greater than 1.0 has above average
risk. Its returns would be more volatile than the market returns. For example,
when market returns move up by five per cent, a stock with beta of 1.5 would
find its returns moving up by 7.5 per cent (i.e. 5 × 1.5). Similarly, decline in
market returns by five per cent would produce a decline of 7.5 per cent in the
return of the individual security.
A stock with beta less than 1.0 would have below average risk. Variability in
its returns would be comparatively lesser than the market variability. Beta can
also be negative, implying that the stock returns move in a direction opposite
to that of the market returns.
Beta is calculated from historical data of returns to measure the systematic
risk of a security. It is a historical measure of systematic risk. In using this
beta for investment decision-making, the investor is assuming that the
relationship between the security variability and market variability will
continue to remain the same in future also.
To conclude, risk is the possibility of variation in returns from an investment.
Many factors contribute to this variability in returns. Some of these factors
are system-wide and affect all securities, while some are unique and affect
only specific securities. Total variability or risk of a security can be measured
by calculating the standard deviation or variance of the security’s returns.
Beta measures the systematic risk of a security.
VALUE AT RISK (VaR) ANALYSIS
Value-at-Risk (VaR) is a novel concept of measuring risk associated with
investment. Risk is related to the variability of returns from an investment.
Risk or the possibility of incurring a loss arises when there is an adverse
movement in the asset value. Standard deviation which is the most popular
measure of variability does not consider the direction of movement; it
measures the total variability in returns, which could be both favourable and
unfavourable. VaR is a measure which specifically focuses on the downside
risk in investment.
Origin
VaR has emerged as a risk assessment tool at banks and other financial
services firms since the early 1990s. The term value-at-risk and the usage of
the VaR measure can be traced back to the RiskMetrics service offered by
J.P. Morgan, a globally diversified commercial bank, in 1995. RiskMetrics
service provided public access to data on the variances of and covariances
across various security and asset classes that the bank had been using
internally for risk management. The data enabled the users to calculate the
risk assessment measure called VaR. J.P. Morgan released the first detailed
description of value-at-risk titled RiskMetrics Technical Document as part of
its free RiskMetrics service. Value-at-risk was rapidly embraced as the tool of
choice for quantifying investment risk.
Concept
Risk has two components: (i) exposure to loss or decline in value and (ii)
uncertainty regarding the future value. Risk metrics or measures used to
quantify risk may be of three types: (i) those that quantify exposure, (ii) those
that quantify uncertainty, (iii) those that quantify exposure and uncertainty in
some combined form. VaR is a risk metrics that quantifies both exposure and
uncertainty.
An Investor often asks the question: “what is the most I can lose on this
investment?” He is interested in knowing the worst-case scenario. As the
future is uncertain, he would also like to know the probability of the worst-
case scenario. VaR is a measure that is designed to answer these questions.
VaR is a measure of the worst possible outcome, expressed with the
probability of its occurrence. VaR measures the potential loss in the value of
a risky asset or portfolio over a specified period expressed with a confidence
level. A typical VaR metrics has three parameters:
1. The amount of potential loss (loss amount or loss percentage).
2. The probability of the loss occurring (confidence level).
3. The time frame (or horizon).
Example
An example can be used to explain the concept of VaR. An investment
portfolio held by an investment fund has calculated its 1 day VaR as ` 50
lakhs with 95 per cent confidence level. It implies that the maximum loss that
the portfolio will suffer on a single day will be limited to (or will be less
than) ` 50 lakhs in 95 out of 100 trading days. The loss is likely to exceed `
50 lakhs only in 5 out of 100 trading days. That is to say that there is 95 per
cent confidence that the value of the portfolio will decrease only by less than
` 50 lakhs on a single trading day. However, there is 5 per cent probability
that the value of the portfolio may decline by more than ` 50 lakhs on a single
trading day.
Thus, VaR calculates the maximum loss expected (or the worst-case
scenario) on an investment over a given time period with a specified degree
of confidence. It is defined as: “the expected loss from an adverse market
movement with a specified probability over a period of time”.
Methods
Three methods are generally used for calculating VaR. These methods are:
1. Historical method (Historical simulation)
2. Variance-covariance method (Parametric method)
3. Monte Carlo simulation method
It is necessary to understand the assumptions and methodology of each
method.
Historical method
This method assumes that history will repeat itself. The data set used for
calculation of VaR in this method is the historical returns (daily or monthly)
of the investment for a fairly long time period, say 5 to 10 years. These
historical returns are rearranged in ascending order from the worst to the best.
VaR focuses on the worst returns. A histogram of the rearranged data can be
used to identify the worst 5 per cent or 1 per cent of returns from the left tail
of the histogram. Mathematically, the 5th percentile or 1st percentile of the
historical returns can be calculated to find the VaR metrics. The 5th
percentile indicates the VaR metrics of 95 per cent confidence level; whereas
the 1st percentile indicates the VaR metrics of 99 per cent confidence level.
The worst-case scenario of the historical data is assumed to repeat in the
future time period also.
Parametric method
This method assumes that the investment returns are normally distributed.
For a given set of daily or monthly return data, two statistical measures are
estimated: the expected return (mean return) and the variability of returns
(standard deviation of returns). VaR metrics are calculated for different
confidence levels using the standard deviation of returns (SD) and the critical
values (z values) from the Standard Normal Distribution curve (or table).
The z values for different confidence levels are as follows:
90 per cent confidence level = 1.28
95 per cent confidence level = 1.645
99 per cent confidence level = 2.326
VaR metrics for different confidence levels are calculated by multiplying the
corresponding Critical value and the Standard Deviation of returns.
VaR (95 per cent confidence level) = 1.645 × SD
VaR (99 per cent confidence level) = 2.326 × SD
The return data may be calculated for different time periods such as daily,
weekly, monthly, yearly, etc. Hence, VaR metrics can also be calculated for
different time periods. But, VaR metrics calculated for one time period can be
easily converted into VaR metrics for another period. For example, daily VaR
metrics can be converted into monthly VaR metrics. This conversion is done
using the square root rule which says that the T-period volatility is equal to
the one period volatility (Standard deviation) multiplied by the square root of
T.
For example, daily volatility or standard deviation of returns of 1.5 per cent is
equivalent to annual volatility of 23.72 per cent, assuming that there are 250
trading days (1.5 ×
= 23.72).
For converting daily VaR into annual VaR, the daily SD has to be first
converted into annual SD and then multiplied with the required z value.
Example
A mutual fund holds an investment portfolio having a market value of ` 30
lakhs. The standard deviation of daily returns of the investment portfolio is
0.64 per cent. Trading days in a month are 20. You are required to calculate
the monthly VaR with 99 per cent confidence level.
Daily SD = 0.64 per cent
Monthly SD = Daily SD ×
= 0.64 ×
= 2.86 per cent
Monthly VaR (99 per cent confidence level) = 2.326 × SD = 2.326 × 2.86 =
6.65 per cent
This is the VaR metrics in percentage terms.
VaR metrics in amount or currency units can be calculated by multiplying the
value of the investment with the VaR percentage.
Thus, VaR (amount) = ` 30,00,000 × 6.65 per cent = ` 1,99,500
Monte Carlo simulation method
The method is based on the historical data of investment returns. The Monte
Carlo simulation procedure is used to develop a model for future investment
returns by running multiple hypothetical trials or simulations with the
historical data. The worst 5 per cent or 1 per cent outcome from the model
gives the respective VaR metrics.
The three methods are likely to give different results. The Parametric method
is the easiest of the three methods, while Monte Carlo simulation is the most
complex method. The Historical method requires manipulation of large
historical data.
Evaluation
VaR analysis is called the “new science of risk management”. The concept of
Value-at-Risk is simple to understand and has an intuitive appeal. However,
as a meaningful measure of investment risk, it has certain limitations. VaR
has a narrow focus with a narrow definition of risk. It is exclusively focused
on downside risk, and even within that downside risk, only at a very small
slice of it. There is no single precise method for measuring VaR; hence, there
can be no unique value for the VaR metrics. All methods of calculation use
historical data in some form; but historical data may not serve as a good
predictor of future outcomes.
SOLVED EXAMPLES
Example 1 A share is ` currently selling at 50. It is expected that a dividend
of ` 2 per share would be paid during the year and the share could be sold at `
54 at the end of the year. Calculate the expected return from the share.
Example 2 Calculate the expected return and the standard deviation of
returns for a stock having the following probability distribution of returns.
Possible returns (in per cent)
Probability of occurrence
−25
0.05
−10
0.10
0
0.10
15
0.15
20
0.25
30
0.20
35
0.15
Example 3 A stock costing ` 120 pays no dividends. The possible prices that
the stock might sell for at the end of the year with the respective probabilities
as follows:
Price (` )
Probability
115
0.1
120
0.1
125
0.2
130
0.3
135
0.2
140
0.1
1. Calculate the expected return.
2. Calculate the standard deviation of returns.
Solution Here, the probable returns have to be calculated using the formula
Calculation of Probable Returns
Possible prices (P1)
P1 − P0
[(P1 − P0)/P0] × 100
`
`
Return (per cent)
115
−5
−4.17
120
0
0.00
125
5
4.17
130
10
8.33
135
15
12.50
140
20
16.67
Calculation of Expected Return
Calculation of Standard Deviation of Returns
Example 4 An investor has analysed a share for a one-year holding period.
The share is currently selling for ` 43 but pays no dividends and there is a
fifty-fifty chance that the share will sell for either ` 55 or ` 60 by the year end.
What is the expected return and risk if 250 shares are acquired with 80 per
cent borrowed funds? Assume the cost of borrowed funds to be 12 per cent.
(Ignore commissions and taxes).
Example 5 Monthly return data (in per cent) are presented below for ITC
stock and BSE National Index for a 12 month period.
Month
ITC
BSE National Index
1
9.43
7.41
2
0.00
−5.33
3
−4.31
−7.35
4
−18.92
−14.64
5
−6.67
1.58
6
26.57
15.19
7
20.00
5.11
8
2.93
0.76
9
5.25
−0.97
10
21.45
10.44
11
23.13
17.47
12
32.83
20.15
Calculate beta of ITC stock.
Calculation of Correlation Coefficient
Example 6 With the data given in example 5, calculate beta of ITC stock,
using the regression model.
Solution
Dependent variable Y = Ri
Independent variable X = Rm
From the table prepared for solving the problem in example 5, we have the
following values:
Example 7 Monthly return data (in per cent) for ONGC stock and the NSE
index for a 12 month period are presented below:
Month
ONGC
NSE Index
1
−0.75
−0.35
2
5.45
−0.49
3
−3.05
−1.03
4
3.41
1.64
5
9.13
6.67
6
2.36
1.13
7
−0.42
0.72
8
5.51
0.84
9
6.80
4.05
10
2.60
1.21
11
−3.81
0.29
12
−1.91
−1.96
1. Calculate alpha and beta for the ONGC stock.
2. Suppose NSE index is expected to move up by 15 per cent next month.
How much return would you expect from ONGC?
Solution Since alpha and beta of the stock are to be calculated, the regression
model may be used.
The expected return from ONGC stock when NSE index moves up by 15 per
cent can be calculated from the regression equation which is
Ri = 0.67 + 1.359 Rm
Substituting the value of Rm as 15 in the equation, we get
Ri = 0.67 + 1.359 (15) = 0.67 + 20.385 = 21.055
EXERCISES
1. Calculate the expected return and the standard deviation of returns for a
stock having the following probability distribution:
Probable returns (per cent)
Probability of Occurrence
− 24
0.05
− 10
0.15
0
0.15
12
0.20
18
0.20
22
0.15
30
0.10
2. A stock costing ` 250 pays no dividends. The possible prices that the
stock might sell for at the end of the year and the probability of each are:
Possible prices (`)
Probability
200
0.10
230
0.25
250
0.35
280
0.20
310
0.10
(a) What is the expected return?
(b) What is the standard deviation of the returns?
3. An investor has analysed a stock for a one-year holding period. There is a
fifty-fifty chance that the stock, currently selling at ` 60, will sell for ` 55 or
` 70 by the year end. The investor can borrow on 40 per cent margin from
his bank at 10 per cent per annum.
(a) What are the investor’s expected holding period yield and risk if he
buys 100 shares and does not borrow?
(b) What would be his expected yield and risk if he buys 200 shares
paying 60 per cent of the cost with borrowed funds?
4. Monthly return data (in per cent) for IPCL stock and the NSE index for a
12 month period are presented as follows:
Month
IPCL
NSE Index
1
10.27
11.00
2
9.31
3.69
3
6.73
4.20
4
−5.68
−4.93
5
2.60
3.05
6
2.86
5.88
7
2.78
3.74
8
3.84
2.63
9
−6.51
−2.10
10
−23.42
−21.35
11
0.00
−4.55
12
6.64
2.80
Calculate beta of IPCL stock.
REVIEW QUESTIONS
1. What is the meaning of risk?
2. Explain the concept of systematic risk. Why is it called systematic risk?
3. Write notes on:
(a) Interest rate risk
(b) Market risk
(c) Purchasing power risk
4. “The market price of bonds is inversely related to the market interest
rates.” Explain.
5. What is unsystematic risk? Explain the different types of unsystematic
risk.
6. “Financial risk is a function of financial leverage.” Explain.
7. Explain the mean-variance approach to estimation of return and risk of a
security.
8. What is Beta? How is it interpreted?
REFERENCES
1. Rao, Ramesh K.S. 1989, Fundamentals of Financial Management, p.
389, Macmillan, New York.
2. Ibid., p. 416.
FUNDAMENTAL ANALYSIS:
ECONOMY ANALYSIS
The primary motive of buying a share is to sell it subsequently at a higher
price. In many cases, dividends are also expected. Thus, dividends and price
changes constitute the return from investing in shares. Consequently, an
investor would be interested to know the dividend to be paid on the share in
the future as also the future price of the share. These values can only be
estimated and not predicted with certainty. These values are primarily
determined by the performance of the company which in turn is influenced
by the performance of the industry to which the company belongs and the
general economic and socio-political scenario of the country.
An investor who would like to be rational and scientific in his investment
activity has to evaluate a lot of information about the past performance and
the expected future performance of companies, industries and the economy as
a whole before taking the investment decision. Such evaluation or analysis is
called fundamental analysis.
MEANING OF FUNDAMENTAL ANALYSIS
Fundamental analysis is really a logical and systematic approach to
estimating the future dividends and share price. It is based on the basic
premise that share price is determined by a number of fundamental factors
relating to the economy, industry and company. Hence, the economy
fundamentals, industry fundamentals and company fundamentals have to be
considered while analysing a security for investment purpose. Fundamental
analysis is, in other words, a detailed analysis of the fundamental factors
affecting the performance of companies.
Each share is assumed to have an economic worth based on its present and
future earning capacity. This is called its intrinsic value or fundamental value.
The purpose of fundamental analysis is to evaluate the present and future
earning capacity of a share based on the economy, industry and company
fundamentals and thereby assess the intrinsic value of the share. The investor
can then compare the intrinsic value of the share with the prevailing market
price to arrive at an investment decision. If the market price of the share is
lower than its intrinsic value, the investor would decide to buy the share as it
is underpriced. The price of such a share is expected to move up in future to
match with its intrinsic value.
On the contrary, when the market price of a share is higher than its intrinsic
value, it is perceived to be overpriced. The market price of such a share is
expected to come down in future and hence, the investor would decide to sell
such a share. Fundamental analysis thus provides an analytical framework for
rational investment decision-making. This analytical framework is known as
EIC framework, or economy-industry-company analysis.
Fundamental analysis insists that no one should purchase or sell a share on
the basis of tips and rumours. The fundamental approach calls upon the
investor to make his buy or sell decision on the basis of a detailed analysis of
the information about the company, the industry to which the company
belongs, and the economy. This results in informed investing. For this, a
fundamentalist makes use of the EIC framework of analysis.
ECONOMY-INDUSTRY-COMPANY
FRAMEWORK
ANALYSIS
The analysis of economy, industry and company fundamentals constitute the
main activity in the fundamental approach to security analysis. These can be
viewed as different stages in the investment decision-making process and can
be depicted graphically with three concentric circles as shown in Fig. 7.1.
In this era of globalisation we may add one more circle to the diagram to
represent the international economy.
The logic of this three tier analysis is that the company performance depends
not only on its own efforts, but also on the general industry and economy
factors. A company belongs to an industry and the industry operates within
the economy. As such, industry and economy factors affect the performance
of the company. The multitude of factors affecting the performance of a
company can be broadly classified as:
1. Economy-wide factors such as growth rate of the economy, inflation
rate, foreign exchange rates, etc. which affect all companies.
2. Industry-wide factors such as demand-supply gap in the industry, the
emergence of substitute products, changes in government policy relating
to the industry, etc. These factors affect only those companies belonging
to a specific industry.
3. Company-specific factors such as the age of its plant, the quality of
management, brand image of its products, its labour-management
relations, etc. These factors are likely to make a company’s performance
quite different from that of its competitors in the same industry.
Fundamental analysis thus involves three steps:
1. Economy Analysis
2. Industry Analysis
3. Company Analysis.
Let us see what each of these analyses implies.
ECONOMY ANALYSIS
The performance of a company depends on the performance of the economy.
If the economy is booming, incomes rise, demand for goods increases, and
hence the industries and companies in general tend to be prosperous. On the
other hand, if the economy is in recession, the performance of companies will
be generally bad.
Investors are concerned with those variables in the economy which affect the
performance of the company in which they intend to invest. A study of these
economic variables would give an idea about future corporate earnings and
the payment of dividends and interest to investors.
Let us look at some of the key economic variables that an investor must
monitor as part of his fundamental analysis.
Growth Rates of National Income
The rate of growth of the national economy is an important variable to be
considered by
an investor. GNP (gross national product), NNP (net national product) and
GDP (gross domestic product) are the different measures of the total income
or total economic output of the country as a whole. The growth rates of these
measures indicate the growth rate of the economy. The estimates of GNP,
NNP and GDP and their growth rates are made available by the government
from time to time.
The estimated growth rate of the economy would be a pointer towards the
prosperity of the economy. An economy typically passes through different
phases of prosperity, known as the different stages of the economic or
business cycle. The four stages of an economic cycle are depression,
recovery, boom and recession. The stage of the economic cycle through
which a country passes has a direct impact on the performance of industries
and companies.
Depression is the worst of the four stages. During a depression, demand is
low and declining. Inflation is often high and so are interest rates. Companies
are forced to reduce production, shut down plant and lay off workers.
During the recovery stage, the economy begins to revive after a depression.
Demand picks up leading to more investments in the economy. Production,
employment and profits are on the increase.
The boom phase of the economic cycle is characterised by high demand.
Investments and production are maintained at a high level to satisfy the high
demand. Companies generally post higher profits. The boom phase gradually
slows down. The economy slowly begins to experience a downturn in
demand, production, employment, etc. The profits of companies also start to
decline. This is the recession stage of the business cycle.
While analysing the growth rate of the economy, an investor would do well
to determine the stage of the economic cycle through which the economy is
passing and evaluate its impact on his investment decision.
Infation
Inflation prevailing in the economy has considerable impact on the
performance of companies. Higher rates of inflation upset business plans,
lead to cost escalation and result in a squeeze on profit margins. On the other
hand, inflation leads to erosion of purchasing power in the hands of
consumers. This will result in lower demand for products. Thus, high rates of
inflation in an economy are likely to affect the performance of companies
adversely. Industries and companies prosper during times of low inflation.
Inflation is measured both in terms of wholesale prices through the wholesale
price index (WPI) and in terms of retail prices through the consumer price
index (CPI). These figures are available on weekly or monthly basis. As part
of the fundamental analysis, an investor should evaluate the inflation rate
prevailing in the economy currently as also the trend of inflation likely to
prevail in the future.
Interest Rates
Interest rates determine the cost and availability of credit for companies
operating in an economy. A low interest rate stimulates investment by
making credit available easily and cheaply. Moreover, it implies lower cost of
finance for companies and thereby assures higher profitability. On the
contrary, higher interest rates result in higher cost of production which may
lead to lower profitability and lower demand.
The interest rates in the organised financial sector of the economy are
determined by the monetary policy of the government and the trends in
money supply. These rates are thus controlled and vary within certain ranges.
But the interest rates in the unorganised financial sector are not controlled
and may fluctuate widely depending upon the demand and supply of funds in
the market. Further, long-term interest rates differ from short-term interest
rates.
An investor has to consider the interest rates prevailing in the different
segments of the economy and evaluate their impact on the performance and
profitability of companies.
Government Revenue, Expenditure and Deficits
As the government is the largest investor and spender of money, the trends in
government revenue, expenditure and deficits have a significant impact on
the performance of industries and companies. Expenditure by the government
stimulates the economy by creating jobs and generating demand. Since a
major portion of demand in the economy is generated by government
spending, the nature of government spending is of great importance in
determining the fortunes of many an industry.
However, when government expenditure exceeds its revenue, there occurs a
deficit. This deficit is known as budget deficit. All developing countries
suffer from budget deficits as governments spend large amounts of money to
build up infrastructure. But budget deficit is an important determinant of
inflation, as it leads to deficit financing which fuels inflation.
The budget document contains detailed information on each item of
government expenditure and revenue and the resulting deficit. An investor
has to evaluate these carefully to assess their impact on his investments.
Exchange Rates
The performance and profitability of industries and companies that are major
importers or exporters are considerably affected by the exchange rates of the
rupee against major currencies of the world. A depreciation of the rupee
improves the competitive position of Indian products in foreign markets,
thereby stimulating exports. But it would also make imports more expensive.
A company depending heavily on imports may find devaluation of the rupee
affecting its profitability adversely.
The exchange rates of the rupee are influenced by the balance of trade
deficit, the balance of payments deficit and also the foreign exchange
reserves of the country. The excess of imports over exports is called balance
of trade deficit. The balance of payments deficit represents the net difference
payable on account of all transactions such as trade, services and capital
transactions. If these deficits increase, there is a possibility that the rupee may
depreciate in value.
A country needs foreign exchange reserves to meet several commitments
such as payment for imports and servicing of foreign debts. Balance of
payment deficit typically leads to decline in foreign exchange reserves as the
deficit has to be met from the reserve. The size of the foreign exchange
reserve is a measure of the strength of the rupee on external account. Large
foreign exchange reserves help to increase the value of the rupee against
other currencies.
The exchange rates of the rupee against the major currencies of the world are
published daily in the financial press. An investor has to keep track of the
trend in exchange rates of rupee. An analysis of the balance of trade deficit,
balance of payments deficit and the foreign exchange reserves will help to
project the future trends in exchange rates.
Infrastructure
The development of an economy depends very much on the infrastructure
available. Industry needs electricity for its manufacturing activities, roads and
railways to transport raw materials and finished goods, communication
channels to keep in touch with suppliers and customers. The availability of
infrastructural facilities such as power, transportation and communication
systems affects the performance of companies. Bad infrastructure leads to
inefficiencies, lower productivity, wastage and delays. An investor should
assess the status of the infrastructural facilities available in the economy
before finalising his investment plans.
Monsoon
The Indian economy is essentially an agrarian economy and agriculture forms
a very important sector of the Indian economy. Because of the strong forward
and backward linkages between agriculture and industry, performance of
several industries and companies are dependent on the performance of
agriculture. Moreover, as agricultural incomes rise, the demand for industrial
products and services will be good and industry will prosper.
But the performance of agriculture to a very great extent depends on the
monsoon. The adequacy of the monsoon determines the success or failure of
the agricultural activities in India. Hence, the progress and adequacy of the
monsoon becomes a matter of great concern for an investor in the Indian
context.
Economic and Political Stability
A stable political environment is necessary for steady and balanced growth.
No industry or company can grow and prosper in the midst of political
turmoil. Stable long-term economic policies are what are needed for
industrial growth. Such stable policies can emanate only from stable political
systems as economic and political factors are inter-linked. A stable
government with clear cut long-term economic policies will be conducive to
good performance of the economy.
ECONOMIC FORECASTING
Economy analysis is the first stage of fundamental analysis and starts with an
analysis of historical performance of the economy. But as investment is a
future-oriented activity, the investor is more interested in the expected future
performance of the overall economy and its various segments. For this,
forecasting the future direction of the economy becomes necessary.
Economic forecasting thus becomes a key activity in economy analysis.
The central theme in economic forecasting is to forecast the national income
with its various components. Gross national product or GNP is a measure of
the national income. It is the total value of the final output of goods and
services produced in the economy. It is a measure of the total economic
activities over a specified period of time and is an indicator of the level and
rate of growth of economic activities. An investor would be particularly
interested in forecasting the various components of the national income,
especially those components that have a bearing on the particular industries
and companies that he is analysing.
FORECASTING TECHNIQUES
Economic forecasting may be carried out for short-term periods (up to three
years), intermediate term periods (three to five years) and long-term periods
(more than five years). An investor is more concerned about short-term
economic forecasts for periods ranging from a quarter to three years. Some of
the techniques of short-term economic forecasting are discussed below:
Anticipatory Surveys
Much of the activities in government, business, trade and industry are
planned in advance and stated in the form of budgets. Consumers also plan
for their major spending in advance. To the extent that institutions and people
plan and budget for expenditures in advance, surveys of their intentions can
provide valuable input to short-term economic forecasting.
Anticipatory surveys are the surveys of intentions of people in government,
business, trade and industry regarding their construction activities, plant and
machinery expenditures, level of inventory, etc. Such surveys may also
include the future plans of consumers with regard to their spending on
durables and non-durables. Based on the results of these surveys, the analyst
can form his own forecast of the future state of the economy.
The greatest shortcoming of the anticipatory surveys is that there is no
guarantee that the intentions surveyed will certainly materialise. The forecast
based on anticipatory surveys or surveys of intentions will be valid only to
the extent that the intentions are translated into action. Hence, the analyst
cannot rely solely on these surveys.
Barometric or Indicator Approach
In this approach to economic forecasting, various types of indicators are
studied to find out how the economy is likely to perform in the future. These
indicators are time series data of certain economic variables. The indicators
are classified into leading, coincidental and lagging indicators.
The leading indicators are those time series data that reach their high points
(peaks) or their low points (troughs) in advance of the high points and low
points of total economic activity. The coincidental indicators reach their
peaks and troughs at approximately the same time as the economy, while the
lagging indicators reach their turning points after the economy has already
reached its own turning points. In this method, the indicators act as
barometers to indicate the future level of economic activity. However, careful
examination of historical data of economic series is necessary to ascertain
which economic variables have led, lagged behind or moved together with
the economy.
The US Department of Commerce, through its Bureau of Economic Analysis,
has prepared a short list of the different indicators. Some of them are given
below for illustrative purpose.1
Leading Indicators
Average weekly hours of manufacturing production workers
Average weekly initial unemployment claims
Contracts and orders for plant and machinery
Number of new building permits issued
Index of S and P 500 stock prices
Money supply (M2)
Change in sensitive materials prices
Change in manufacturers’ unfilled orders (durable goods industries)
Index of consumer expectations
Coincidental Indicators
Employees on non-agricultural pay rolls
Personal income less transfer payments
Index of industrial production
Manufacturing and trade sales
Lagging Indicators
Average duration of unemployment
Ratio of manufacturing and trade inventories to sales
Average prime rate
Commercial and industrial loans outstanding
Change in consumer price index for services
Of the three types of indicators, leading indicators are more useful for
economic forecasting because they measure something that foreshadows a
change in economic activity.
The indicator approach has its own limitations. It is useful in forecasting the
direction of a change in aggregate economic activity, but it does not indicate
the magnitude or duration of the change. Further, the leading indicators may
give false signals. Moreover, different leading indicators may give conflicting
signals. The indicator approach becomes useful for economic forecasting
only if data collection and presentation are done quickly. Any delay in
presentation of data defeats the purpose of the indicators.
Econometric Model Building
This is the most precise and scientific of the different forecasting techniques.
This technique makes use of Econometrics, which is a discipline that applies
mathematical and statistical techniques to economic theory.
In the economic field we find complex interrelationships between the
different economic variables. The precise relationships between the
dependent and independent variables are specified in a formal mathematical
manner in the form of equations. The system of equations is then solved to
yield a forecast that is quite precise.
In applying this technique, the analyst is forced to define clearly and
precisely the interrelationships between the economic variables. The accuracy
of the forecast derived from this technique would depend on the validity of
the assumptions made by the analyst regarding economic interrelationships
and the quality of his input data.
Econometric models used for economic forecasting are generally complex.
Vast amounts of data are required to be collected and processed for the
solution of the model. This may cause delay in making the results available.
Undue delay may render the results obsolete for purpose of forecasting.
Opportunistic Model Building
This is one of the most widely used forecasting techniques. It is also known
as GNP model building or sectoral analysis.
Initially, an analyst estimates the total demand in the economy, and based on
this he estimates the total income or GNP for the forecast period. This initial
estimate takes into consideration the prevailing economic environment such
as the existing tax rates, interest rates, rate of inflation and other economic
and fiscal policies of the government. After this initial forecast is arrived at,
the analyst now begins building up a forecast of the GNP figure by estimating
the levels of various components of GNP. For this, he collects the figures of
consumption expenditure, gross private domestic investment, government
purchase of goods and services and net exports. He adds these figures
together to arrive at the GNP forecast.
The two GNP forecasts arrived at by two different methods will be compared
and necessary adjustments will be made to bring the two forecasts into line
with each other.
The opportunistic model building approach makes use of other forecasting
techniques to build up the various components. A vast amount of judgement
and ingenuity is also applied to make the overall forecast reliable.
Economic forecasting is an extremely complex and difficult process. No
method is expected to give accurate results. The investor must evaluate all
economic forecasts critically before making his investment decision.
Economy analysis is an important part of fundamental analysis. It gives the
investor an overall picture of the expected performance of the economy in the
near future. This is a valuable input to investment decision-making.
REVIEW QUESTIONS
1. What is fundamental analysis?
2. “Fundamental analysis provides an analytical framework for rational
investment decision-making.” Explain.
3. Describe the key economic variables that an investor must monitor as
part of his fundamental analysis.
4. Explain the impact of the following economic variables on the
performance of the economy and the companies:
(a) Interest rates
(b) Government revenue, expenditure and deficits
(c) Infrastructure
5. What is the significance of economic forecasting in fundamental
analysis?
6. Briefly describe the techniques of short-term economic forecasting.
7. Explain the barometric or indicator approach to economic forecasting.
REFERENCE
1. Fischer, Donald E. and Ronald J. Jordan, 1994, Security Analysis and
Portfolio Management, 5th ed., p. 144, Prentice-Hall of India, New
Delhi.
INDUSTRY AND COMPANY
ANALYSIS
INDUSTRY ANALYSIS
An investor ultimately invests his money in the securities of one or more
specific companies. Each company can be characterised as belonging to an
industry. The performance of companies would, therefore, be influenced by
the fortunes of the industry to which it belongs. For this reason an analyst has
to undertake an industry analysis so as to study the fundamental factors
affecting the performance of different industries.
At any stage in the economy, there are some industries which are fast
growing while others are stagnating or declining. If an industry is growing,
the companies within the industry may also be prosperous. The performance
of companies will depend, among other things, upon the state of the industry
to which they belong. Industry analysis refers to an evaluation of the relative
strengths and weaknesses of particular industries.
Concept of Industry
An industry is generally described as a homogenous group of companies. We
may define an industry “as a group of firms producing reasonably similar
products which serve the same needs of a common set of buyers.”1 Industries
are traditionally classified on the basis of products. According to this
product-wise classification we have cement industry, steel industry, cotton
textile industry, pharmaceutical industry, and so forth. However, industry
classification becomes difficult when dealing with firms having a diversified
product line. And such firms are now on the increase. Even though
classification of industry poses practical difficulties, each country follows a
standardised classification to facilitate data collection and reporting.
Industry Life Cycle
Marketing experts believe that each product has a life cycle. They have
identified four stages in the life of a product, namely introduction stage,
growth stage, maturity stage and the decline stage. In the same way, an
industry is also said to have a life cycle. This industry life cycle theory is
generally attributed to Julius Grodinsky. According to the industry life cycle
theory, the life of an industry can be segregated into the pioneering stage, the
expansion stage, the stagnation stage, and the decay stage. This kind of
segregation is extremely useful to an investor because the profitability of an
industry depends upon its stage of growth. In fact, each development stage is
unique and exhibits different characteristics.
Technological advances in one industry can effect the growth of another
industry. The jute industry began to decline when alternate and cheaper
packing materials came into use. The popularity of synthetic textiles can
adversely affect the demand for cotton textiles, and vice versa.
The first step in industry analysis, therefore, is to determine the stage of
growth through which the industry is passing.
Pioneering Stage
This is the first stage in the industrial life cycle of a new industry where the
technology as well as the product are relatively new and have not reached a
state of perfection. The pioneering stage is characterised by rapid growth in
demand for the output of industry. As a result there is a great opportunity for
profit. Many companies compete with each other vigorously. As large
number of companies attempt to capture their share of the market, there arises
high business mortality rates. Weak firms are eliminated and a lesser number
of firms survive the pioneering stage.
An example of the pioneering stage of an industry was the leasing industry
which was establishing itself during the mid eighties. There was a mushroom
growth of leasing companies in India during this period. Initially, high lease
rentals were charged by these companies. But as competition increased, lease
rentals were reduced. Many companies which could not operate profitably
with the low levels of lease rentals were closed down. Leasing industry in
India today is much pruned compared to what it was in the mideighties.
It is difficult for the analyst to identify those companies that are likely to
survive and come out strongly later on. Therefore, investment in companies
in an industry that is in the pioneering stage is highly risky. Industries in the
pioneering stage are called sunrise industries. Telecommunications,
computer software, information technology, etc. are examples of sunrise
industries in India at present.
Expansion Stage
Once an industry has established itself it enters the second stage of expansion
or growth. The industry now includes only those companies that have
survived the pioneering stage. These companies continue to become stronger.
Each company finds a market for itself and develops its own strategies to sell
and maintain its position in the market. The competition among the surviving
companies brings about improved products at lower prices.
Companies in the expansion stage of an industry are quite attractive for
investment purposes. Investors can get high returns at low risk because
demand exceeds supply in this stage. Companies will earn increasing
amounts of profits and pay attractive dividends.
Stagnation Stage
This is the third stage in the industry life cycle. In this stage, the growth of
the industry stabilises. The ability of the industry to grow appears to have
been lost. Sales may be increasing but at a slower rate than that experienced
by competitive industries or by the overall economy. The industry begins to
stagnate. The transition of the industry from the expansion stage to the
stagnation stage is often very slow. Two important reasons for this transition
are change in social habits and development of improved technology.
The black and white television industry in India provides a good example of
an industry which passed from the expansion stage to the stagnation stage
during the eighties. Sometimes an industry may stagnate only for a short
period. By the introduction of a technological innovation or a new product, it
may resume a process of growth, thereby starting a new cycle. Therefore, an
investor or analyst has to monitor the industry developments constantly and
with diligence. An investor should dispose of his holdings in an industry
which begins to pass from the expansion stage to the stagnation stage because
what is to follow is the decay of the industry.
Decay Stage
From the stagnation stage the industry passes to the decay stage. This occurs
when the products of the industry are no longer in demand. New products and
new technologies have come to the market. Customers have changed their
habits, style and liking. As a result, the industry becomes obsolete and
gradually ceases to exist. Thus, changes in social habits, changes in
technology and declining demand are the causes of decay of an industry. An
investor should get out of the industry before the onset of the decay stage.
The industry life cycle approach has important implications for the investor.
It gives an insight into the apparent merits of investment in a given industry
at a given time. An industry usually exhibits low profitability in the
pioneering stage, high profitability in the growth or expansion stage, medium
but steady profitability in the stagnation or maturity stage and declining
profitability in the decay stage. The profit associated with the different stages
in the life of an industry can be illustrated in the form of an inverted ‘S’ curve
as shown in Fig. 8.1.
Even though the industry life cycle approach provides a useful framework for
industry analysis by an investor, its limitations should not be overlooked. It is
not always easy to detect which stage of development an industry is in at any
point in time. The transition from one stage to the next is slow and unclear. It
can be detected only by careful analysis. Further, the classification of
industries under this approach is the general pattern. There can be exceptions
to this general pattern. The life of an industry may, for instance, be extended
after the stagnation and decay stage through appropriate adaptation to
changes in the environment. Careful analysis is needed to detect such
exceptions.
Industry Characteristics
In an industry analysis, there are a number of key characteristics that should
be considered by the analyst. These features broadly relate to the operational
and structural aspects of the industry. They have a bearing on the prospects of
the industry. Some of these are discussed below:
Demand Supply Gap
The demand for a product usually tends to change at a steady rate, whereas
the capacity to produce the product tends to change at irregular intervals,
depending upon the installation of additional production capacity. As a result,
an industry is likely to experience under-supply and over-supply of capacity
at different times. Excess supply reduces the profitability of the industry
through a decline in the unit price realisation. On the contrary, insufficient
supply tends to improve the profitability through higher unit price realisation.
Therefore, the gap between demand and supply in an industry is a fairly good
indicator of its short-term or medium-term prospects. As part of industry
analysis, an investor should estimate the demand supply gap in the industry.
Competitive Conditions in the Industry
Another significant factor to be considered in industry analysis is the
competitive conditions in the industry. The level of competition among
various companies in an industry is determined by certain competitive forces.
These competitive forces are: barriers to entry, the threat of substitution,
bargaining power of the buyers, bargaining power of the suppliers and the
rivalry among competitors.
New entrants to an industry increase the capacity in an industry. But these
new entrants may face certain barriers to their entry. The barriers to entry
may arise because of product differentiation, absolute cost advantage or
economy of scale. Product differentiation refers to the preference buyers
have for the products of established firms. Their products enjoy a premium in
the market. Absolute cost advantage refers to the ability of established firms
to produce their products at a lower cost than any new entrant. Economy of
scale refers to the situation in which it is necessary to attain a fairly high level
of production in order to obtain economically feasible levels of cost. In some
industries it may not be economical to set up small capacities. An industry
which is well protected from the inroads of new firms would be ideal for
investment.
New inventions are always taking place and new and better products are
replacing the existing ones. An industry that can be replaced by substitutes or
is threatened by substitutes is in a weak competitive position. The prospects
of such an industry cannot be considered promising.
In an industry where buyers’ market prevails, the buyers have more
bargaining power. They would demand better quality and better services;
they would also force down the prices, eroding profitability in the industry.
Thus, an industry which is dictated by buyers would be in a weak competitive
position. On the contrary, an industry where the sellers have higher
bargaining power is expected to do well and be in a stronger position.
Where supply exceeds demand and there are many competing firms, the
rivalry among the competing firms in an industry is likely to increase. This
will lead to price cuts and heavy advertising as each competing firm tries to
capture a larger market share. In such a situation, the companies in the
industry lose their competitive edge and their profitability gets eroded.
Permanence
In this age of rapid technological change, the degree of permanence of an
industry is an important consideration in industry analysis. Permanence is a
phenomenon related to the products and the technology used by the industry.
If an analyst feels that the need for a particular industry will vanish in a short
period, or that the rapid technological changes would render the products
obsolete within a short time, it would be foolish to invest in such an industry.
Labour Conditions
The state of labour conditions in the industry under analysis is an important
consideration in an economy such as ours where the labour unions are very
powerful. If the labour in a particular industry is rebellious and is inclined to
resort to strikes frequently, the prospects of that industry cannot become
bright.
Attitude of Government
The attitude of the government towards an industry has a significant impact
on its prospects. The government may encourage the growth of certain
industries and can assist such industries through favourable legislation.
On the contrary, the government may look with disfavour on certain other
industries. In India, this has been the experience of alcoholic drinks and
cigarette industries. The government may place different kinds of legal
restrictions on its development. A prospective investor should, therefore,
consider the role the government is likely to play in the industry—whether it
will support the industry or will restrain the industry's development through
restrictive legislation.
Supply of Raw Materials
The availability of raw materials is an important factor determining the
profitability of an industry. Some industries may have no difficulty in
obtaining the major raw materials as they may be indigenously available in
plenty. Other industries may have to depend on a few manufacturers within
the country or on imports from outside the country for their raw material
supply. Industry analysis must take into consideration the availability of raw
materials and its impact on industry prospects.
Cost Structure
Another factor to be considered in industry analysis is the cost structure of
the industry, viz. the proportion of fixed costs to variable costs. The higher
the fixed cost component, higher is the sales volume necessary to achieve
break-even point. Conversely, the lower the proportion of fixed cost relative
to variable cost, lower would be the break-even point. Lower break-even
point provides higher margin of safety. An analyst would consider favourably
an industry that has a lower break-even point.
An analyst must evaluate all the above factors before making an investment
decision. If the above factors indicate that the industry has favourable future
prospects, funds may be committed to that industry.
COMPANY ANALYSIS
Company analysis is the final stage of fundamental analysis. The economy
analysis provides the investor a broad outline of the prospects of growth in
the economy. The industry analysis helps the investor to select the industry in
which investment would be rewarding. Now he has to decide the company in
which he should invest his money. Company analysis provides the answer to
this question.
Company analysis deals with the estimation of return and risk of individual
shares. This calls for information. Many pieces of information influence
investment decisions. Information regarding companies can be broadly
classified into two broad groups: internal and external. Internal information
consists of data and events made public by companies concerning their
operations. The internal information sources include annual reports to
shareholders, public and private statements of officers of the company, the
company’s financial statements, etc. External sources of information are
those generated independently outside the company. These are prepared by
investment services and the financial press.
In company analysis, the analyst tries to forecast the future earnings of the
company because there is strong evidence that earnings have a direct and
powerful effect upon share prices. The level, trend and stability of earnings of
a company, however, depend upon a number of factors concerning the
operations of the company.
Financial Statements
The prosperity of a company would depend upon its profitability and
financial health. The financial statements published by a company
periodically help us to assess the profitability and financial health of the
company. The two basic financial statements provided by a company are the
balance sheet and the profit and loss account. The first gives us a picture of
the company’s assets and liabilities while the second gives us a picture of its
earnings.
The balance sheet gives the list of assets and liabilities of a company on a
specific date. The major categories of assets are fixed assets and current
assets. Fixed assets are those assets which are intended to be used up over a
period of several years. Current assets are those assets which are intended to
be converted into cash in the near future (within one year). The major
categories of liabilities are outside liabilities and liability towards share
holders. The outside liabilities are categorised as short-term and long-term
liabilities. The short-term liabilities which are expected to be paid off within
the next one year are known as current liabilities. The balance sheet
indicates the financial position of a company on a particular date, namely the
last day of the accounting year.
The profit and loss account, also called income statement, reveals the
revenue earned, the cost incurred and the resulting profit or loss of the
company for one accounting year. The profit after tax (PAT) divided by the
number of shares gives the earnings per share (EPS) which is a figure in
which most investors are interested. The profit-and-loss account summarises
the activities of a company during an accounting year.
Analysis of Financial Statements
The financial statements of a company can be used to evaluate the financial
performance of the company. Financial ratios are most extensively used for
the purpose. Ratio analysis helps an investor to determine the strengths and
weaknesses of a company. It also helps him to assess whether the financial
performance and financial strength are improving or deteriorating. Ratios can
be used for comparative analysis either with other firms in the industry
through a cross sectional analysis or with the past data through a time series
analysis.
Different ratios measure different aspects of a company’s performance or
health. Four groups of ratios may be used for analysing the performance of a
company.
Liquidity Ratios
These measure the company’s ability to fulfil its short-term obligations and
reflect its short-term financial strength or liquidity. The commonly used
liquidity ratios are:
A higher current ratio would enable a company to meet its short-term
obligations even if the value of current assets declines. The quick ratio
represents the ratio between quick assets and current liabilities. It is a more
rigorous measure of liquidity. However, both these ratios are to be used
together to analyse the liquidity of a company.
Leverage Ratios
These ratios are also known as capital structure ratios. They measure the
company’s ability to meet its long-term debt obligations. They throw light on
the long-term solvency of a company. The commonly used leverage ratios are
the following:
The first three ratios indicate the relative contribution of owners and creditors
in financing the assets of the company. These ratios reflect the safety margin
available to the long-term creditors. The coverage ratio measures the ability
of the company to meet its interest payments arising from the debt.
Profitability Ratios
The profitability of a company can be measured by the profitability ratios.
These ratios are calculated by relating the profits either to sales, or to
investment, or to the equity shares. Thus, we have three groups of
profitability ratios. These are listed below.
The overall profitability is measured by the return on investment, which is the
product of net profit ratio and investment turnover. It is a central measure of
the earning power or operating efficiency of a company.
Activity or Efficiency Ratios
These are also known as turnover ratios. These ratios measure the efficiency
in asset management. They express the relationship between sales and the
different types of assets, showing the speed with which these assets generate
sales. Important activity ratios are enumerated below.
Ratio analysis is a method of interpreting the financial statements of a
company. A single ratio by itself is not of much use. A comprehensive
evaluation of the financial performance of a company emerges only from a
study of all the important ratios.
Ratios calculated from the financial statements reveal the performance during
the past years. For an investor what is important is the future prospects of a
company and not its past achievements. From an analysis of past
performance, the analyst has to forecast the future prospects of the company.
The investment decision would depend on such forecast.
Other Variables
The future prospects of a company would also depend upon a number of
other variables, some of which are given below.
1. Company's market share
2. Capacity utilisation
3. Modernisation and expansion plans
4. Order book position
5. Availability of raw materials
Some of these informations may be available in the directors’ report and the
chairman’s speech at the annual general meeting of the company. Others may
be available in financial journals and magazines.
The most important variable affecting the future prospects of a company is
perhaps the quality of its management. But assessing the quality and
competence of management is perhaps the most difficult task in company
analysis. Some critical aspects of a company’s management which every
investor must consider carefully are their commitment and competence,
professionalism, future orientation, image building, investor friendliness and
government relation building. The future of a company depends on the
quality and competence of its management to a very great extent.
Assessment of Risk
Company analysis involves not only an estimation of future returns, but also
an assessment of the variability in returns called risk. The variability in
returns arises primarily because of variability in sales. The sensitivity of
profits to changes in the level of sales is measured by a ratio called degree of
total leverage (DTL). This ratio is used as a measure of risk. It is calculated
as follows:
It may be noted that contribution means sales minus the variable costs.
DTL may be subdivided into two components: (a) the degree of operating
leverage (DOL) arising from the cost structure of the company, and (b) the
degree of financial leverage (DFL) arising from the capital structure of the
company.
DOL measures the percentage change in EBIT for a one per cent change in
sales and is computed as:
The degree of total leverage (DTL) is the product of DOL and DFL and
measures the percentage change in PBT for a one per cent change in sales.
The investment decision is ultimately a decision to invest in the shares of one
or more specific companies. Company analysis deals with an analysis of
various factors affecting the performance of companies so as to forecast the
future earnings of a company as also its variability better known as risk.
REVIEW QUESTIONS
1. What is industry analysis?
2. Explain the concept of industry life cycle. Describe the different stages
in the industry life cycle.
3. “The first step in industry analysis is to determine the stage of growth
through which the industry is passing.” Explain.
4. What are sunrise industries? Describe their characteristics.
5. Describe the various characteristics of an industry that an analyst must
consider while doing industry analysis.
6. How does the competitive condition in an industry affect the
performance of the industry?
7. What is company analysis? Explain how financial ratios can be used to
determine the strengths and weaknesses of a company.
8. “The level, trend and stability of earnings of a company depend upon a
number of factors concerning the operations of the company.” Discuss.
REFERENCE
1. Barua, Samir K., et al., 1996, Portfolio Management, 1st rev. ed., p. 76,
Tata McGraw-Hill, New Delhi.
SHARE VALUATION
Fundamental analysis is based on the premise that each share has an intrinsic
worth or value which depends upon the benefits that the holder of a share
expects to receive in future from the share in the form of dividends and
capital appreciation. The investment decision of the fundamental analyst to
buy or sell a share is based on a comparison between the intrinsic value of a
share and its current market price. If the market price of a share is currently
lower than its intrinsic value, such a share would be bought because it is
perceived to be underpriced. A share whose current market price is higher
than its intrinsic value would be considered as overpriced and hence sold.
The fundamental analyst believes that the market price of a share is a
reflection of its intrinsic value. Though, in the short run, the market price
may deviate from intrinsic value, in the long run the price would move along
with the intrinsic value of the share. The investment decision of the
fundamental analyst is based on this belief regarding the relationship between
market price and intrinsic value.
The market price of a share and its intrinsic value are thus the two basic
inputs necessary for the investment decision. Market price of a share is
available from the quotations of stock exchanges. The intrinsic value is
estimated through the process of stock or share valuation.
CONCEPT OF PRESENT VALUE
The present value concept is a fundamental concept used in the share
valuation procedure. An understanding of this concept is necessary for
studying the share valuation process.
Money has a ‘time value’. This implies that a rupee received now is worth
more than a rupee to be received after one year, because the rupee received
now can be deposited in a bank at 10 per cent interest rate to receive ` 1.10
after one year. The time value of money suggests that earlier receipts are
more desirable than later receipts, because earlier receipts can be reinvested
to generate additional returns before the later receipts come in.
If an amount P is invested now for n years at r rate of interest, the future
value F to be received after n years can be calculated using the compound
interest formula.
F = P(1 + r)n
For example, if ` 1000 is invested in a bank for three years at 10 per cent
interest, the amount to be received after the three year period would be
calculated as:
F = 1000(1.1)3 = ` 1331
Thus, the future value of a present sum can be calculated by the
compounding process. Similarly, the present value of a sum to be received in
future can be calculated by a reverse process known as discounting. For
example, we may want to know what amount is to be deposited in the bank at
10 per cent to receive ` 500 after one year.
This can be calculated by the formula, namely:
The present value of a future sum is the amount to be invested now to
accumulate to that sum in the future. ` 413.22 invested now at 10 per cent
interest would grow to ` 500 by the end of two years. Obviously, the present
value of future sums would be lower than those future sums.
SHARE VALUATION MODEL
The valuation model used to estimate the intrinsic value of a share is the
present value model. The intrinsic value of a share is the present value of all
future amounts to be received in respect of the ownership of that share,
computed at an appropriate discount rate.
The major receipts that come from the ownership of a share are the annual
dividends and the sale proceeds of the share at the end of the holding period.
These are to be discounted to find their present value, using a discount rate
that is the rate of return required by the investor, taking into consideration the
risk involved and the investor's other investment opportunities. Thus, the
intrinsic value of a share is the present value of all the future benefits
expected to be received from that share.
One Year Holding Period
It is easy to start share valuation with one year holding period assumption.
Here an investor intends to purchase a share now, hold it for one year and sell
it off at the end of one year. In this case, the investor would be expected to
receive an amount of dividend as well as the selling price after one year. The
present value of the share may be expressed as:
where
D1 = Amount of dividend expected to be received at the end of one year.
S1 = Selling price expected to be realised on sale of the share at the end of
one year.
k = Rate of return required by the investor.
For example, if an investor expects to get ` 3.50 as dividend from a share next
year and hopes to sell off the share at ` 45 after holding it for one year, and if
his required rate of return is 25 per cent, the present value of this share to the
investor can be calculated as follows:
This is the intrinsic value of the share. The investor would buy this share only
if its current market price is lower than this value.
Multiple-year Holding Period
An investor may hold a share for a certain number of years and sell it off at
the end of his holding period. In this case, he would receive annual dividends
each year and the sale price of the share at the end of the holding period. The
present value of the share may be expressed as:
where
D1, D2, D3, ... , Dn = Annual dividends to be received each year.
Sn = Sale price at the end of the holding price.
k = Investor’s required rate of return.
n = Holding period in years.
For example, if an investor expects to get ` 3.50, ` 4 and ` 4.50 as dividend
from a share during the next three years and hopes to sell it off at ` 75 at the
end of the third year, and if his required rate of return is 25 per cent, the
present value of this share to the investor can be calculated as follows:
In order to use the present value model for share valuation, the investor has to
forecast the future dividends as well as the selling price of the share at the
end of his holding period. It is not possible to forecast these variables
accurately. Hence, this model is practically infeasible. Modifications of this
model have been developed to render it useful for practical purposes of stock
valuation.
In the case of most equity shares, the dividend per share grows because of the
growth in earnings of a company. In other words, equity dividends grow and
are not constant over time. The growth rate pattern of equity dividends have
to be estimated. Different assumptions about the growth rate patterns can be
made and incorporated into the valuation models. Two assumptions that are
commonly used are:
1. Dividends grow at a constant rate in future, i.e. the constant growth
assumption.
2. Dividends grow at varying rates in future, i.e. multiple growth
assumption.
These two assumptions give rise to two modified versions of the present
value model of share valuation: (a) Constant growth model, and (b) Multiple
growth model.
CONSTANT GROWTH MODEL
In this model it is assumed that dividends will grow at the same rate (g) into
the indefinite future and that the discount rate (k) is greater than the dividend
growth rate (g). By applying the growth rate (g) to the current dividend (D0),
the dividend expected to be received after one year (D1) can be calculated as:
D1 = D0(1 + g)1
The dividend expected to be received after two years, three years, etc. can
also be calculated from the current dividend as:
D2 = D0(1 + g)2
D3 = D0(1 + g)3
Dn = D0(1 + g)n
The present value model for share valuation may now be ritten as:
When ‘n’ approaches infinity, this formula can be simplified as:
Thus, according to this model, the intrinsic value of a share is equal to next
year’s expected dividend divided by the difference between the appropriate
discount rate for the stock and its expected dividend growth rate.
The constant growth model is also known as Gordon’s share valuation
model, named after the model’s originator, Myron J. Gordon. This is one of
the most well-known and widely used models because of its simplicity. The
model does not require forecasts of future dividends and future selling price
of the share. All that the model requires is a dividend growth rate assumption
and a discount rate. Both of these can be estimated without much difficulty.
The growth rate may be estimated from past growth rates of dividends and
earnings. The discount rate is the investor’s required rate of return which is
somewhat subjective and would depend upon the investor’s alternative
investment opportunities and his perception of risk involved in purchasing
the share.
To illustrate the application of Gordon share valuation model, let us consider
an example. A company has declared a dividend of ` 2.50 per share for the
current year. The company has been following a policy of enhancing its
dividends by 10 per cent every year and is expected to continue this policy in
the future also. An investor who is considering the purchase of the shares of
this company has a required rate of return of 15 per cent.
The intrinsic value of the company’s share can be calculated as:
The investor would be advised to purchase the share if the current market
price is lower than ` 55.
MULTIPLE GROWTH MODEL
The constant growth assumption may not be realistic in many situations. The
growth in dividends may be at varying rates. A typical situation for many
companies may be that a period of extraordinary growth (either good or bad)
will prevail for a certain number of years, after which growth will change to a
level at which it is expected to continue indefinitely. This situation can be
represented by a two-stage growth model.
In this model, the future time period is viewed as divisible into two different
growth segments, the initial extraordinary growth period and the subsequent
constant growth period. During the initial period growth rates will be variable
from year to year, while during the subsequent period the growth rate will
remain constant from year to year. The investor has to forecast the time N
upto which growth rates would be variable and after which the growth rate
would be constant. This would mean that the present value calculations will
have to be spread over two phases, where one phase would last until time N
and the other would begin after time N to infinity.
The intrinsic value of the share is then the sum of the present values of two
dividend flows: (a) the flow from period 1 to N which we will call V1, and (b)
the flow from period N + 1 to infinity, referred to as V2. This means,
S0 = V1 + V2
The growth rates during the first phase of extraordinary growth is likely to be
variable from year to year. Hence, the expected dividend for each year during
the first phase may be forecast individually. The multiple year holding period
valuation model may be used for this first phase, using the dividend forecasts
developed for each of the years in the first phase. Then
The second phase present value is denoted by V2 and would be based on the
constant growth model, because the dividend growth is assumed to be
constant during the second phase. The position of the investor at time N, after
which the second phase commences, can be viewed as a point in time when
he is forecasting a stream of dividends for time periods N + 1, N + 2, N + 3
and so on, which grow at a constant rate, g. The second phase dividends
would be:
DN+1 = DN (1 + g)1
DN+2 = DN (1 + g)2
DN+3 = DN (1 + g)3
and so on to infinity.
The present value of the second phase stream of dividends from period N + 1
to infinity can be calculated using Gordon share valuation model as:
It may be noted that this value is the present value at time N of all future
expected dividends from time period N + 1 to infinity. When this value has to
be viewed at time ‘zero’, it must be discounted to provide the present value at
‘zero’ time for the second phase dividend stream. When so discounted the
present value of the second phase dividend stream viewed at ‘zero’ time may
be expressed as:
The present values of the two phases, V1 and V2, may be added to provide the
intrinsic value of the share that has a two-stage growth.
The summation procedure of the two phases may be expressed as:
To illustrate the two-stage growth model, let us consider an example.
A company paid a dividend of ` 1.75 per share during the current year. It is
expected to pay a dividend of ` 2 per share during the next year. Investors
forecast a dividend of ` 3 and ` 3.50 per share respectively during the two
subsequent years. After that it is expected that annual dividends will grow at
10 per cent per year into an indefinite future.
If the investor’s required rate of return is 20 per cent, the intrinsic value of the
share can be calculated as shown below.
In this, the dividend growth rate is variable upto the third year. From the
fourth year onwards dividend growth rate is constant. V1 would be the present
value of dividends receivable during the first three years and can be
calculated as:
DISCOUNT RATE
The discount rate used in the present value models is the investor’s required
rate of return. This has to take into consideration the time value of money as
well as the risk of the security in which investment is proposed to be made.
The time value of money is represented by the risk-free interest rate such as
those on government securities. A premium is added to this risk-free interest
rate to take care of the risk to be borne by the investor by investing in the
particular share. The more risky the investment, the greater the risk premium
that the investor will require. The assessment of risk and the estimation of
risk premium required are usually done by investors on a subjective basis.
Though other objective methods are available for the purpose, they are not
popularly used. Thus, the investor’s required rate of return would comprise
the risk-free interest rate plus a risk premium.
The present value models discussed above are also known as dividend
discounted valuation models because they discount the stream of dividends
expected to be received from a share in the future.
MULTIPLIER APPROACH TO SHARE VALUATION
Many investors and analysts value shares by estimating an appropriate
multiplier for the share. The price-earnings ratio (P/E ratio) is the most
popular multiplier used for the purpose.
The price-earnings ratio is given by the expression:
The intrinsic value of a share is taken as the current earnings per share or the
forecasted future earnings per share times the appropriate P/E ratio for the
share. For example, if the current EPS of a share is ` 8 and if the investor
feels that the appropriate P/E ratio for the share is 12, then the intrinsic value
of the share would be taken as ` 96. Investment decision to buy or sell the
share would be taken after comparing this intrinsic value with the current
market price of the share.
The major difficulty for the analyst using the multiplier approach to share
valuation is the determination of an appropriate price-earnings ratio for the
share. Different approaches may be adopted for the determination of the
appropriate P/E ratio. It may be arrived at by the analyst on a subjective basis
based on his evaluation of various fundamental factors relating to the
company. The major factors considered would be growth rate in earnings and
the risk factor. The higher the expected growth and the lower the risk, the
greater would be the appropriate price-earnings ratio for the share.
Another approach would be to use the historical P/E ratios of the company
itself or the P/E ratios of other companies in the same industry. In the first
case, the mean of the historical P/E ratios of the company in the past may be
taken as the appropriate P/E ratio for share valuation. In the latter case, the
median P/E ratio of companies in the same industry may be taken as the
appropriate P/E ratio.
REGRESSION ANALYSIS
Still another approach to the determination of an appropriate P/E ratio is a
statistical approach. The broad determinants of share prices such as earnings,
growth, risk and dividend policy may be used to estimate the appropriate P/E
ratio with the help of statistical analysis. The analyst identifies the factors
(known as independent variables) which influence the share price (the
dependent variable) and then ascertains the relationship between these factors
and the share price. The relationship that exists at any point in time between
the share price or price-earnings ratio and the set of specified determining
variables can be estimated using multiple regression analysis. The resulting
regression equation measures the simultaneous impact of the determining
variables on the price-earnings ratio. This equation can be used to arrive at
the appropriate P/E ratio for the share. By substituting the values of the
determining variables for a share, the appropriate P/E ratio for the share can
be easily calculated.
One of the earliest attempts to use multiple regression to explain priceearnings ratios, which received wide attention, was Whitbeck-Kisor model.
Whitbeck and Kisor set out to measure the relationship of the P/E ratio of a
stock to its dividend policy, growth and risk. They used dividend pay outs,
earnings growth rates and the variation (standard deviation) of growth rates to
measure the determining variables. Then, using multiple regression analysis
to define the average relationship between each of these variables and price
earnings ratios, they found (as of June 8, 1962) that
P/E ratio = 8.2 + 1.5 (earnings growth rate) + 0.067 (dividend pay out rate) −
0.2 (standard deviation in growth rate)
The numbers in the equation are the regression coefficients. 8.2 is the
constant term and the other numbers represent the weightage of the respective
independent variables or factors influencing the P/E ratio.
This equation could be used to determine the appropriate P/E ratio of a stock.
For example, if there is a share with a growth forecast of 7 per cent, dividend
pay out of 40 per cent and standard deviation in growth rate amounting to 12,
the appropriate P/E ratio for this share would be
8.2 + 1.5(7) + 0.067(40) − 0.2(12) = 18.98
Many models of this nature have been developed since then. But the major
drawback of these regression models is that they are appropriate only for the
time period used and the sample used.
Share valuation is an integral part of fundamental analysis. It was Benjamin
Graham and David Dodd who pioneered the development of systematic
methods of security evaluation in their book Security Analysis published in
1934. Share valuation deals with the determination of the theoretical or
normative price of a share, the price that a share should sell for, better
known as the intrinsic value of the share. This price is then compared with
the actual price of the share prevailing in the market to arrive at the
appropriate investment decision. Share valuation, however, is a difficult
exercise. Different approaches may be adopted for the purpose, but all of
them require forecasts of fundamental data about companies. No valuation
model can produce good results if the forecasts on which it is based are of
poor quality.
SOLVED EXAMPLES
Example 1 Consider five annual cash flows (the first occurring one year from
today)
Year:
1
2
3
4
5
Cash flow (`):
5
8
12
15
16
Given a discount rate of 10 per cent, what is the present value of this stream
of cash flows?
9
Example 2 A share is currently selling for ` 65. The company is expected to
pay a dividend of ` 2.50 on the share at the end of the year. It is reliably
estimated that the share will sell for ` 78 at the end of the year.
1. Assuming that the dividend and price forecasts are accurate, would you
buy the share to hold it for one year, if your required rate of return were
12 per cent?
2. Given the current price of ` 65 and the expected dividend of ` 2.50, what
would the price have to be at the end of one year to justify purchase of
the share today, if your required rate of return were 15 per cent?
We have to determine the selling price at the end of the year (S1) which will
give the intrinsic value of the share as ` 65.
A selling price of ` 72.25 at the end of the year would justify the purchase of
the share at the current price of ` 65.
Example 3 You have decided to buy 500 shares of an IT company with the
intention of selling out at the end of five years. You estimate that the
company will pay ` 3.50 per share as dividends for the first two years and `
4.50 per share for the next three years. You further estimate that, at the end of
the five year holding period, the shares can be sold for ` 85. What would you
be willing to pay today for these shares if your required rate of return is 12
per cent?
Solution The share valuation model for multi-year holding period is:
The maximum price to be paid for the shares would be ` 62.76 per share.
Example 4 A company paid a cash dividend of ` 4 per share on its stock
during the current year. The earnings and dividends of the company are
expected to grow at an annual rate of 8 per cent indefinitely. Investors expect
a rate of return of 14 per cent on the company’s shares. What is a fair price
for this company’s shares?
Solution The valuation model to be applied in this case is the constant growth
model which is:
Example 5 A company paid dividends amounting to ` 0.75 per share during
the last year. The company is expected to pay ` 2 per share during the next
year. Investors forecast a dividend of ` 3 per share in the year after that.
Thereafter, it is expected that dividends will grow at 10 per cent per year into
an indefinite future. Would you buy/sell the share if the current price of the
share is ` 54? Investor’s required rate of return is 15 per cent.
Example 6 A chemical company paid a dividend of ` 2.75 during the current
year. Forecasts suggest that earnings and dividends of the company are likely
to grow at the rate of 8 per cent over the next five years and at the rate of 5
per cent thereafter. Investors have traditionally required a rate of return of 20
per cent on these shares. What is the present value of the stock?
Solution The valuation model to be applied in this case is the two-stage
growth model
Given
D0 = ` 2.75
N=5
k = 20 per cent
g (for the first five years) = 8 per cent
g (after five years) = 5 per cent
S0 = V1 + V2 = 10.13 + 11.36 = 21.49
The present value of the stock is ` 21.49.
Example 7 Cement products Ltd. currently pays a dividend of ` 4 per share
on its equity shares.
1. If the company plans to increase its dividend at the rate of 8 per cent per
year indefinitely, what will be the dividend per share in 10 years?
2. If the company’s dividend per share is expected to be ` 7.05 per share at
the end of five years, at what annual rate is the dividend expected to
grow?
EXERCISES
1. An IT company currently pays a dividend of ` 5 per share on its equity
shares. The dividend is expected to grow at 6 per cent per year
indefinitely. Stocks with similar risk currently are priced to provide a 12
per cent expected return. What is the intrinsic value of the stock?
2. Alfa Ltd. paid a dividend of ` 2 per share for the current year. A constant
growth in dividend of 10 per cent has been forecast for an indefinite
future period. Investor’s required rate of return has been estimated to be
15 per cent. The current market price of the share is ` 60. Would you buy
the share?
3. A company recently paid an annual dividend on its stock of ` 3 per share.
The dividend is expected to grow at ` 1 per share for the next four years.
Thereafter, the dividend is expected to grow at 6 per cent per year
indefinitely. The required return on stocks with similar risk is 15 per
cent. What is the intrinsic value of the stock?
4. A company is expecting to declare a dividend of ` 3.50 per share during
the next year. Investors forecast a dividend of ` 4 in the year after that,
and ` 4.50 in the next year. Thereafter, it is expected that dividends will
grow at 10 per cent per year into an indefinite future. The investor’s
required rate of return is 20 per cent. What is the maximum price that an
investor should pay for the share?
5. Telstar Ltd. just paid ` 3.33 as dividend. The company had paid a
dividend of ` 2.25 eight years ago. What has been the annual growth rate
in dividends during this period? If the growth rate continues to be the
same, how much will you be willing to pay for a share if you require a
return of 12 per cent?
6. Computech Ltd. paid a dividend of ` 1.50 five years ago and has just
paid an annual dividend of ` 2.42; you expect dividends to grow at the
same annual rate for the next four years. After that, you expect dividends
to grow at an annual rate of 15 per cent. How much will you be willing
to pay for a share if you require 20 per cent rate of return?
REVIEW QUESTIONS
1. Explain the concept of ‘present value’.
2. How would you estimate the intrinsic value of a share which is to be
held for one year?
3. Explain Gordon’s share valuation model with suitable illustration. What
are the advantages of this model?
4. Illustrate the two-stage growth model of share valuation with an
example.
5. How would you determine the discount rate to be applied in the present
value models of share valuation?
6. Describe the multiplier approach to share valuation.
10
BOND VALUATION
Bonds are long-term fixed income securities. Debentures are also long-term
fixed income securities. Both of these are debt securities. In India, debt
securities issued by the government and public sector units are generally
referred to as bonds, while debt securities issued by private sector joint stock
companies are called debentures. The two terms, however, are often used
interchangeably. The term ‘bond’ is used in this chapter to include debentures
also.
The two major categories of bonds are government bonds and corporate
bonds. Government bonds represent the borrowings of the government. Since
they are backed by the government, they are considered free from default
risk. Corporate bonds represent debt obligations of private sector companies.
Corporate bonds are backed by the credit of the issuing companies. It is the
company’s ability to earn money and meet the debt obligations that
determines the bond’s default risk.
In the case of bonds, both the cash flow streams (interest and principal) and
the time horizon (maturity) are well specified and fixed. This makes bond
valuation easier than stock valuation. Nevertheless, certain special features of
bonds such as callability and convertibility may make bond valuation
complex. In the case of callable bonds, the bonds may be called for
redemption earlier than its maturity date. As the right to call rests with the
companies, callable bonds must offer a higher interest to compensate for
disadvantageous calls. Convertible bonds are those that can be converted into
equity shares at a later date either fully or partly. Because the option to
convert often rests with the bond holder, the interest offered on the bond can
be less as part of the return is the value of the option.
Bond valuation is less glamorous than stock valuation for two reasons. First,
the returns from investing in bonds are less impressive and fixed. Second,
bond prices fluctuate less than equity prices. As the uncertainty associated
with the cash flows occurring to a bond holder is less, the emphasis is more
on fine-tuned calculations and analysis. An investor in bonds should be on
the look out for even small differentials in prices and returns.
BOND RETURNS
Bond returns can be calculated and expressed in different ways. It is
necessary to understand the meaning of each of these expressions.
Coupon Rate
It is the nominal rate of interest fixed and printed on the bond certificate. It is
calculated on the face value of the bond. It is the rate at which interest is
payable by the issuing company to the bondholder. For example, if the
coupon rate on a bond of face value of ` 1000 is 12 per cent, ` 120 would be
payable by the company to the bondholder annually till maturity.
Current Yield
The current market price of a bond in the secondary market may differ from
its face value. A bond of face value ` 100 may be selling at a discount, at say
` 90, or it may be selling at a premium at ` 115.
The current yield relates the annual interest receivable on a bond to its current
market price. It can be expressed as follows:
The current yield would be higher than the coupon rate when the bond is
selling at a discount as in our example. Current yield would be lower than the
coupon rate for a bond selling at a premium.
The current yield measures the annual return accruing to a bondholder who
purchases the bond from the secondary market and sells it before maturity,
presumably at the same price at which he bought the bond. It does not
measure the entire returns accruing from a bond held till maturity. More
specifically, it does not consider the reinvestment of annual interest received
from the bond and the capital gain or loss realised on maturity of the bond.
The bond holder in our example would realise a capital gain of ` 200 on
maturity, as the bond which was purchased from the market for ` 800 would
be redeemed at the face value of ` 1000 on maturity.
Spot Interest Rate
Zero coupon bond is a special type of bond which does not pay annual
interests. The return on this bond is in the form of a discount on issue of the
bond. For example, a two-year bond of face value ` 1000 may be issued at a
discount for ` 797.19. The investor who purchases this bond for ` 797.19 now
would receive ` 1000 two years later. This type of bond is also called pure
discount bond or deep discount bond. The return received from a zero
coupon bond or a pure discount bond expressed on an annualised basis is the
spot interest rate. In other words, spot interest rate is the annual rate of return
on a bond that has only one cash inflow to the investor.
Mathematically, spot interest rate is the discount rate that makes the present
value of the single cash inflow to the investor equal to the cost of the bond. In
other words, the cash inflow from the bond when discounted with the spot
interest rate becomes equal to the cost of the bond. Thus, in the case of a two
year bond of face value ` 1000, issued at a discount for ` 797.19,
The spot interest rate is 12 per cent per annum. This is an annual rate.
To understand the calculation of spot interest rate, let us take another
example. Consider a zero coupon bond whose face value is ` 1000 and
maturity period is five years. If the issue price of the bond is ` 519.37, the
spot interest rate can be calculated as shown below:
The spot interest rate in this case is 14 per cent.
Yield to Maturity (YTM)
This is the most widely used measure of return on bonds. It may be defined
as the compounded rate of return an investor is expected to receive from a
bond purchased at the current market price and held to maturity. It is really
the internal rate of return earned from holding a bond till maturity.
The yield to maturity or YTM depends upon the cash outflow for purchasing
the bond, that is, the cost or current market price of the bond as well as the
cash inflows from the bond, namely the future interest payments and the
terminal principal repayment. YTM is the discount rate that makes the
present value of cash inflows from the bond equal to the cash outflow for
purchasing the bond.
The relation between the cash outflow, the cash inflow and the YTM of a
bond can be expressed as:
What is required is a value of YTM that makes the right hand side of the
equation equal to ` 900. Since the market price is lower than the face value, it
indicates that YTM would be higher than the coupon rate.
We may start with 20 per cent as the value of YTM. The right hand side of
the equation then becomes
` 150 × present value annuity factor (5 yrs, 20%) + ` 1000 × present
value factor (5 yrs, 20%) = (150 × 2.9906) + (1000 × 0.4019) = 448.59
+ 401.90 = ` 850.49
Since the value obtained is lower than the current market price of ` 900, a
lower discount rate has to be tried. Taking YTM as 18 per cent, the right hand
side of the equation becomes
(150 × 3.1272) + (1000 × 0.4371) = 469.08 + 437.10 = 906.18
The value obtained is higher than the required amount of ` 900. Hence, YTM
lies between 18 per cent and 20 per cent. It can be estimated using
interpolation as shown below.
The YTM concept is a compound interest concept. It is assumed that all
intermediate cash inflows in the form of interest are reinvested at YTM. The
investor is thus assumed to earn interest on interest at YTM throughout the
holding period. Hence, when the intermediate inflows are reinvested at a rate
lower than YTM, the yield actually realised by the investor would be lower
than YTM.
The tedious calculations involved in determining YTM can be avoided by
using the following formula which gives an approximate estimate of YTM.
Yield to Call (YTC)
Some bonds may be redeemable before their full maturity period either at the
option of the issuer or of the investor. Such option would be exercisable at a
specified period and at a specified price. If the option is exercised, the bond
would be called for redemption at the specified call price on the specified call
date. For example, a company may issue fifteen year bonds which can be
redeemed at the end of five years, at the option of either the investor or the
issuer, at a premium of five per cent on face value.
How do we calculate the yield on such bonds? In such cases, two yields may
be calculated: (a) yield to maturity assuming that the bond will be redeemed
only at the end of the full maturity period (fifteen years in the above
example); (b) yield to call assuming that the bond will be redeemed at the
call date (five years in the above example).
The yield to call is computed on the assumption that the bond’s cash inflows
are terminated at the call date with redemption of the bond at the specified
call price. The present value of the ‘cash flows to call’ can be calculated
using different discount rates. The yield to call is that discount rate which
makes the present value of ‘cash flows to call’ equal to the bond’s current
market price or the cost of purchase of the bond.
If the yield to call is higher than the yield to maturity, it would be
advantageous to the investor to exercise the redemption option at the call
date. If, on the other hand, the yield to maturity is higher, it would be better
to hold the bond till final maturity.
BOND PRICES
All investments, including bonds and shares, derive value from the cash flow
they are expected to generate. Because the cash flows will be received over
future periods, there is need to discount these future cash flows to derive a
present value or price for the security. In general terms, the theoretical price
of any security can be established as the present value of a future stream of
cash flows, as described by the following formula:
The model indicates that the present value or, alternatively, current price P0
of a security is the cash flows (CF) received over the time horizon ‘n’,
discounted back at the rate ‘k’.
The value of a bond is equal to the present value of its expected cash flows.
The cash flows from a bond consist of the annual or semi-annual interest
payments as well as the principal repayment at maturity. In the case of a
bond, these cash flows as well as the time period over which these flows
occur are known. These cash flows have to be discounted at an appropriate
discount rate to determine their present value. The present value calculations
are made with the help of the following equation:
where
P0 = Present value of the bond.
It = Annual interest payments.
MV = Maturity value of the bond.
n = Number of years to maturity.
k = Appropriate discount rate.
For using the above equation, the appropriate discount rate has to be
determined. The current market interest rate which investors can earn on
other comparable investments is the proper discount rate to be used in the
present value model.
Let us consider an example. A bond of face value ` 1000 was issued five
years ago at a coupon rate of 10 per cent. The bond had a maturity period of
10 years and as of today, therefore, five more years are left for final
repayment at par. If the current market interest rate is 14 per cent, the present
value of the bond can be determined as follows:
Most bonds pay interest at half-yearly intervals. Where interest payments are
semi-annual, the PV equation has to be modified as follows:
BOND PRICING THEOREMS
Bonds are generally issued with a fixed rate of interest known as the coupon
rate. This is calculated on the face value of the bond and remains fixed till
maturity. At the time of issue of the bond its coupon rate will generally be
equal to the prevailing market interest rate. As time passes, the market
interest rate may change either upwards or downwards. If the current market
interest rate rises above the coupon rate of a bond, the bond provides a lower
return and hence, becomes less attractive. The price of the bond declines
below its face value. This can be seen in the example considered above. The
current market interest rate (14 per cent) is higher than the coupon rate of 10
per cent. The price of the bond is below its face value.
If the market interest rate declines below the coupon rate, the bond price will
increase and the bond will begin to be sold at a premium on its face value.
Thus, bond prices vary inversely with changes in market interest rates. The
amount of price variation necessary to adjust to a given change in interest
rates is a function of the number of years to maturity. In the case of longmaturity bonds, a change in market interest rate results in a relatively large
price change when compared to a short-maturity bond. In other words, the
long-term bond is more sensitive to interest rate changes than the short-term
bonds, i.e. the long-term bonds generally have greater exposure to interest
rate risk.
The relation between bond prices and changes in market interest rates have
been stated by Burton G. Malkiel in the form of five general principles. These
are known as Bond pricing theorems.1 They explain the bond pricing
behaviour in an environment of changing interest rates.
The five principles are:
1. Bond prices will move inversely to market interest changes.
2. Bond price variability is directly related to the term to maturity; which
means, for a given change in the level of market interest rates, changes
in bond prices are greater for longer-term maturities.
3. A bond’s sensitivity to changes in market interest rate increases at a
diminishing rate as the time remaining until its maturity increases.
4. The price changes resulting from equal absolute increases in market
interest rates are not symmetrical, i.e. for any given maturity, a decrease
in market interest rate causes a price rise that is larger than the price
decline that results from an equal increase in market interest rate.
5. Bond price volatility is related to the coupon rate, which implies that the
percentage change in a bond’s price due to a change in the market
interest rate will be smaller if its coupon rate is higher.
These theorems were derived and proven from the basic bond pricing
equation.
BOND RISKS
Bonds are considered to be less risky than equity shares; nevertheless they
are not entirely risk free. Two types of risk are associated with investment in
bonds, namely default risk and interest rate risk.
Risk is the possibility of variation in returns. The actual returns realised from
a bond may vary from the expected returns either because of a default on the
part of the issuer to pay the interest or principal, or because of changes in
market interest rates. The investor has to assess the impact of these two
sources of risk on the returns from a bond before investing in the bond.
Default Risk
Default risk refers to the possibility that a company may fail to pay the
interest or principal on the stipulated dates. Poor financial performance of the
company leads to such default. A part of the interest and principal may not be
received at all or may be received after a long delay. In either case the
investor suffers a loss which goes to reduce his return from the bond.
Credit rating of Debt securities is a mechanism adopted for assessing the
default risk involved. The credit rating process involves a qualitative analysis
of the company’s business and management and a quantitative analysis of the
company’s financial performance. It also considers the specific features of
the bond being issued.
Credit rating services have developed rapidly in India. Now there are
different institutions engaged in credit rating of debt securities. An investor
may rely on the rating provided by these credit rating agencies or,
alternatively, do his own credit rating, to assess the default risk of a bond.
Interest Rate Risk
Another reason for variation in the returns from bonds is the change in
market interest rates. An investor in bonds receives interest annually or semiannually. He reinvests these interest amounts each year at the market interest
rate. Thus, interest is earned on the interest received from the bonds each
year. Finally, at the end of a certain holding period, the investor may sell off
the bond at a price which is equal to its face value.
During the holding period of a bond, meanwhile, the market interest rates
may change. If the market interest rate moves up, the investor would be able
to reinvest the annual interest received from the bond at a higher rate than
expected. He would gain on his reinvestment activity. But, as bond price and
market interest rate are inversely related, future bond price will decline below
its face value when the market interest rate moves up. Consequently, he
would suffer a loss while selling the bond. If the gain on reinvestment is less
than the loss on sale, the investor will suffer a net loss on account of the rise
in market interest rate.
The opposite would be true when the market interest rate moves down. The
investor would be able to reinvest the interest only at lower rate than what
was expected. However, the bond price will move above its face value as the
market interest rate declines. The investor loses on reinvestment of interest
but gains on selling the bond.
Thus, an investor in bonds faces variations in his returns due to changes in
the market interest rate during his holding period. This is referred to as the
interest rate risk. This variation occurs on account of two factors—the
reinvestment of annual interest and the capital gain or loss on sale of bond at
the end of the holding period. When market interest rate rises, there is a gain
on reinvestment but a loss on sale of bond. The converse is true when the
market interest rate falls.
Thus, the interest rate risk is composed of two risks: reinvestment risk and
price risk. The reinvestment risk and the price risk derived from a change in
the market interest have an opposite effect on the bond returns. For any bond
there is a holding period at which these two effects exactly balance each
other. What is lost on reinvestment is exactly compensated by a capital gain
on sale of bond and vice versa. For this holding period there is no interest rate
risk. This particular holding period at which interest rate risk disappears is
known as the duration of the bond.
An investor can, therefore, eliminate interest rate risk of a bond by holding
the bond for its duration. Where the desired holding period of an investor is
significantly different from the duration of the bond, the bond is subject to
interest rate risk.
BOND DURATION
Duration is the weighted average measure of a bond’s life. The various time
periods in which the bond generates cash flows are weighted according to the
relative size of the present value of those flows.
The formula for computing duration d is:
The equation consists of setting out the series of cash flows, discounting them
and multiplying each discounted flow by the time period in which it occurs.
The sum of these cash flows is then divided by the price of the bond obtained
using the present value model.
The formula for calculating duration may be expressed in a more general
format as follows:
To understand the computation of duration, let us consider an example.
A bond with 12 per cent coupon rate issued three years ago is redeemable
after five years from now at a premium of five per cent. The interest rate
prevailing in the market currently is 14 per cent. The duration of this bond
can be calculated as shown below:
Year
cash flow
PV factor f
(` )
@ 14 per cent
Present value
PV multiplied
1
12
0.8772
10.5264
10.5264
2
12
0.7695
9.2340
18.4680
by year
3
12
0.6750
8.1000
24.3000
4
12
0.5921
7.1052
28.4208
5
12
0.5194
6.2328
31.1640
5
105
0.5194
54.5370
272.6850
95.7354
386.0402
Total
The cash flows for each year are discounted at 14 per cent which is the
market interest rate. The sum of these discounted cash flows or present values
is the price of the bond and it constitutes the denominator of the duration
formula. Each present value is multiplied by the year in which the cash flow
occurs. The sum of these figures constitutes the numerator of the duration
formula. Thus,
The maturity of this bond is five years, while its duration is only 4.03 years.
If this bond is held for 4.03 years the interest rate risk on the bond can be
eliminated. The impact of reinvestment risk and price risk would offset each
other exactly to reduce the interest rate risk to zero. Duration of a bond is
thus the time period at which the price risk and the reinvestment risk of a
bond are of equal magnitude but opposite in direction.
Let us consider another example where a new bond is issued by a company.
The coupon rate is 15 per cent and maturity period is five years. The bond
has a face value of ` 100 redeemable after five years at par. As the bond is
newly issued, the coupon rate will be the same as the market interest rate and
the price of the bond will be equal to the face value. The duration of this bond
is calculated below:
Investors generally pay less attention to debt securities as an investment
avenue. Bond returns are less than stock returns, but then bond investment
involves less risk. Historically, there has been a low correlation between the
returns from stocks and corporate bonds. This implies that combining stocks
and bonds in a portfolio can help to reduce the portfolio’s risk as a whole.
Thus, bonds can play a strategic role in portfolio management. Moreover,
investors can capitalise on bond price movements by trading in bonds. For
this the investor needs to have a proper understanding of bonds, their returns,
risks and valuation or pricing procedures.
SOLVED EXAMPLES
Example 1 Jaya Ltd. has a 14 per cent debenture with a face value of ` 100
that matures at par in 15 years. The debenture is callable in five years at `
114. It currently sells for ` 105. Calculate each of the following for this
debenture:
1. Current yield
2. Yield to call
3. Yield to maturity
We have to find the value of YTC that makes the right hand side of the
equation equal to ` 105. This has to be done through a process of trial and
error. We can use the present value tables for calculation purposes. We may
start with 15 per cent as the value of YTC.
The right hand side of the equation then becomes:
` 14 × present value annuity factor (5 years, 15%) + ` 114 × present value
factor (5 years, 15 %)
= (14 × 3.3522) + (114 × 0.4972) = 46.93 + 56.68 = 103.61
Since the value obtained is lower than the current market price of ` 105, a
lower discount rate has to be tried. Taking YTC as 14 per cent, the right hand
side of the equation becomes:
` 14 × present value annuity factor (5 years, 14%) + ` 114 × present value
factor (5 years, 14%)
= (14 × 3. 4331) + (114 × 0.5194) = 48.03 + 59.21 = 107.24
Example 2 A person owns a ` 1000 face value bond with five years to
maturity. The bond makes annual interest payments of ` 80. The bond is
currently priced at ` 960. Given that the market interest rate is 10 per cent,
should the investor hold or sell the bond?
Solution The intrinsic value of the bond has to be calculated and compared
with the current market price. The value of a bond is equal to the present
value of its expected cash inflow. It can be calculated with the following
formula:
The current market price of the bond (` 960) is higher than its intrinsic value
of ` 924.16. As the bond is overpriced, the investor may sell it.
Example 3 An investor purchases for ` 5555 a zero coupon bond whose face
value is ` 7000 and maturity period is three years. Calculate the spot interest
rate of the bond.
Solution Spot interest rate is the discount rate that makes the present value of
the single cash inflow equal to the cost of the bond, that is,
Example 4 A bond pays interest annually and sells for ` 835. It has six years
left to maturity and a par value of ` 1000. What is its coupon rate if its
promised YTM is 12 per cent?
Example 5 Find the duration of a 6 per cent coupon bond with a face value of
` 1000 making annual interest payments, if it has 5 years until maturity. The
bond is redeemable at 5 per cent premium at maturity. The market interest
rate is currently 8 per cent.
Solution The formula for calculation of the duration of the bond is as
follows:
EXERCISES
1. A bond of ` 1000 was issued five years ago at a coupon rate of 6 per
cent. The bond had a maturity period of 10 years and as of today,
therefore, five more years are left for final repayment at par. The market
interest rate currently is 10 per cent. Determine the value of the bond.
2. A 20 year, 10 per cent coupon interest rate bond has ` 1000 face value.
The market rate of interest is 8 per cent. Compute the intrinsic value of
this bond if it has five years to maturity. Assume that interest is paid
annually.
3. An investor is considering the purchase of a bond currently selling for `
878.50. The bond has four years to maturity, a face value of ` 1000 and a
coupon rate of 8 per cent. The appropriate discount rate for investments
of similar risk is 10 per cent. Calculate the yield to maturity of the bond.
Based on the calculation, should the investor purchase the bond?
4. An investor recently purchased a bond with ` 1000 face value, 10 per
cent coupon rate, and six years to maturity. The bond makes annual
interest payments. The investor paid ` 1032.50 for the bond.
(a) What is the yield to maturity of the bond?
(b) If the bond can be called two years from now at a price of ` 1080,
what is its yield to call?
5. A company issues a deep discount bond of face value of ` 5000 at an
issue price of ` 3550. The maturity period of the bond is 7 years.
Determine the spot interest rate of the bond.
6. Assume a ` 1000 par value bond with 8.5 per cent coupon rate and a
maturity period of 6 years. Determine the duration of the bond, if the
current market interest rate is 10 per cent.
REVIEW QUESTIONS
1. How is the current yield of a bond calculated?
2. What is spot interest rate? Illustrate with an example.
3. What is ‘yield to maturity’? How is it calculated?
4. The value of a bond is equal to the present value of its expected cash
flows. Elucidate with an example.
5. State the principles of the Bond pricing theorem.
6. “Bond prices vary inversely with changes in market interest rates.”
Explain with examples.
7. Write short notes on:
(a) Coupon rate
(b) Yield to call
(c) Zero coupon bond
(d) Default risk of a bond
8. What is interest rate risk of a bond? Explain how the risk arises.
9. What is meant by the duration of the bond? Explain its significance.
REFERENCE
1. Farrell, James L., Jr., 1997, Portfolio Management: Theory and
Application, 2nd ed., pp. 130−132, McGraw-Hill, New York.
11
TECHNICAL ANALYSIS
Prices of securities in the stock market fluctuate daily on account of
continuous buying and selling. Stock prices move in trends and cycles and
are never stable. An investor in the stock market is interested in buying
securities at a low price and selling them at a high price so as to get a good
return on his investment. He, therefore, tries to analyse the movement of
share prices in the market. Two approaches are commonly used for this
purpose. One of these is the fundamental analysis wherein the analyst tries
to determine the true worth or intrinsic value of a share based on the current
and future earning capacity of the company. He would buy the share when its
market price is below its intrinsic value. The second approach to security
analysis is called technical analysis. It is an alternative approach to the study
of stock price behaviour.
MEANING OF TECHNICAL ANALYSIS
A technical analyst believes that share prices are determined by the demand
and supply forces operating in the market. These demand and supply forces
in turn are influenced by a number of fundamental factors as well as certain
psychological or emotional factors. Many of these factors cannot be
quantified. The combined impact of all these factors is reflected in the share
price movement. A technical analyst therefore concentrates on the movement
of share prices. He claims that by examining past share price movements
future share prices can be accurately predicted. Technical analysis is the
name given to forecasting techniques that utilise historical share price data.
The rationale behind technical analysis is that share price behaviour repeats
itself over time and analysts attempt to derive methods to predict this
repetition. A technical analyst looks at the past share price data to see if he
can establish any patterns. He then looks at current price data to see if any of
the established patterns are applicable and, if so, extrapolations can be made
to predict the future price movements. Although past share prices are the
major data used by technical analysts, other statistics such as volume of
trading and stock market indices are also utilised to some extent.
The basic premise of technical analysis is that prices move in trends or waves
which may be upward or downward. It is believed that the present trends are
influenced by the past trends and that the projection of future trends is
possible by an analysis of past price trends. A technical analyst, therefore,
analyses the price and volume movements of individual securities as well as
the market index. Thus, technical analysis is really a study of past or
historical price and volume movements so as to predict the future stock price
behaviour.
Dow Theory
Whatever is generally being accepted today as technical analysis has its roots
in the Dow theory. The theory is so called because it was formulated by
Charles H. Dow who was the editor of the Wall Street Journal in U.S.A. In
fact, the theory was presented in a series of editorials in the Wall Street
Journal during 1900−1902.
Charles Dow formulated a hypothesis that the stock market does not move on
a random basis but is influenced by three distinct cyclical trends that guide its
direction. According to Dow theory, the market has three movements and
these movements are simultaneous in nature. These movements are the
primary movements, secondary reactions and minor movements.
The primary movement is the long range cycle that carries the entire market
up or down. This is the long-term trend in the market. The secondary
reactions act as a restraining force on the primary movement. These are in the
opposite direction to the primary movement and last only for a short while.
These are also known as corrections. For example, when the market is
moving upwards continuously, this upward movement will be interrupted by
downward movements of short durations. These are the secondary reactions.
The third movement in the market is the minor movements which are the
day-to-day fluctuations in the market. The minor movements are not
significant and have no analytical value as they are of very short duration.
The three movements of the market have been compared to the tides, the
waves and the ripples in the ocean.
According to Dow theory, the price movements in the market can be
identified by means of a line chart. In this chart, the closing prices of shares
or the closing values of the market index may be plotted against the
corresponding trading days. The chart would help in identifying the primary
and secondary movements.
Figure 11.1 shows a line chart of the closing values of the market index. The
primary trend of the market is upwards but there are secondary reactions in
the opposite direction. Among the three movements in the market, the
primary movement is considered to be the most important.
The primary trend is said to have three phases in it, each of which would be
interrupted by a counter move or secondary reaction which would retrace
about 33−66 per cent of the earlier rise or fall.
Bullish Trend
During a bull market (upward moving market), in the first phase the prices
would advance with the revival of confidence in the future of business. The
future prospects of business in general would be perceived to be promising.
This will prompt investors to buy shares of companies. During the second
phase, prices would advance due to the improvements in corporate earnings.
In the third phase, prices advance due to inflation and speculation. Thus,
during the bull market, the line chart would exhibit the formation of three
peaks. Each peak would be followed by a bottom formed by the secondary
reaction. Each peak would be higher than the previous peak, each successive
bottom would be higher than the previous bottom. According to Dow theory,
the formation of higher bottoms and higher tops indicates a bullish trend. The
three phases of a bull market are depicted in Fig. 11.2.
Bearish Trend
The bear market is also characterised by three phases. In the first phase,
prices begin to fall due to abandonment of hopes. Investors begin to sell their
shares. In the second phase, companies start reporting lower profits and lower
dividends. This causes further fall in prices due to increased selling pressure.
In the final phase, prices fall still further due to distress selling. A bearish
market would be indicated by the formation of lower tops and lower bottoms.
The three phases of a bear market are depicted in Fig. 11.3.
The Dow theory laid emphasis on volume of transactions also. According to
the theory, volume should expand along the main trend. This means that if
the main trend is bullish, the volume should increase with the rise in prices
and fall during the intermediate reactions. In a bearish market when prices are
falling, the volume should increase with the fall in prices and be smaller
during the intermediate reactions.
The theory also makes certain assumptions which have been referred to as the
hypotheses of the theory.
The first hypothesis states that the primary trend cannot be manipulated. It
means that no single individual or institution or group of individuals and
institutions can exert influence on the major trend of the market. However,
manipulation is possible in the day-to-day or short-term movements in the
market.
The second hypothesis states that the averages discount everything. What it
means is that the daily prices reflect the aggregate judgement and emotions of
all stock market participants. In arriving at the price of a stock the market
discounts (that is, takes into account) everything known and predictable about
the stock that is likely to affect the demand and supply position of the stock.
The third hypothesis states that the theory is not infallible. The theory is
concerned with the trend of the market and has no forecasting value as
regards the duration or the likely price targets for the peak or bottom of the
bull and bear markets.
BASIC PRINCIPLES OF TECHNICAL ANALYSIS
The basic principles on which technical analysis is based may be summarised
as follows:
1. The market value of a security is related to demand and supply factors
operating in the market.
2. There are both rational and irrational factors which surround the supply
and demand factors of a security.
3. Security prices behave in a manner that their movement is continuous in
a particular direction for some length of time.
4. Trends in stock prices have been seen to change when there is a shift in
the demand and supply factors.
5. The shifts in demand and supply can be detected through charts prepared
specially to show market action.
6. Patterns which are projected by charts record price movements and these
recorded patterns are used by analysts to make forecasts about the
movement of prices in future.
Price Charts
Charting represents a key activity in technical analysis, because graphical
representation is the very basis of technical analysis. It is the security prices
that are charted. A share may be traded in the market at different prices on the
same day. Of these different prices prevailing in the market on each trading
day, four prices are important. These are the highest price of the day, the
lowest price of the day, the opening price (first price of the day) and the
closing price (last price of the day). Of these four prices again, the closing
price is by far the most important price of the day because it is the closing
price that is used in most analysis of share prices.
The price chart is the basic tool used by the technical analyst to study the
share price movement. The prices are plotted on an XY graph where the X
axis represents the trading days and the Y axis denotes the prices.
The oldest charting procedure was known as the point and figure (P & F)
charting. It is now out of vogue. Three types of price charts are currently
used by technical analysts. These are the line chart or the closing price chart,
the bar chart and the Japanese candlestick chart.
Line Chart
It is the simplest price chart. In this chart, the closing prices of a share are
plotted on the XY graph on a day to day basis. The closing price of each day
would be represented by a point on the XY graph. All these points would be
connected by a straight line which would indicate the trend of the market. A
line chart is illustrated in Fig. 11.4.
Bar Chart
It is perhaps the most popular chart used by technical analysts. In this chart,
the highest price, the lowest price and the closing price of each day are
plotted on a day-to-day basis. A bar is formed by joining the highest price
and the lowest price of a particular day by a vertical line. The top of the bar
represents the highest price of the day, the bottom of the bar represents the
lowest price of the day and a small horizontal hash on the right of the bar is
used to represent the closing price of the day. Sometimes, the opening price
of the day is marked as a hash on the left side of the bar. An example of a
price bar chart is shown in Fig. 11.5.
Japanese Candlestick Charts
The Japanese candlestick chart shows the highest price, the lowest price, the
opening price and the closing price of shares on a day-to-day basis. The
highest price and the lowest price of a day are joined by a vertical bar. The
opening price and closing price of the day which would fall between the
highest and the lowest prices would be represented by a rectangle so that the
price bar chart looks like a candlestick. Thus, each day’s activity is
represented by a candlestick.
There are mainly three types of candlesticks, viz., the white, the black and the
doji or neutral candlestick. A white candlestick is used to represent a situation
where the closing price of the day is higher than the opening price. A black
candlestick is used when the closing price of the day is lower than the
opening price. Thus, a white candlestick indicates a bullish trend while a
black candlestick indicates a bearish trend. A doji candlestick is the one
where the opening price and the closing price of the day are the same.
Japanese candlestick chart is illustrated in Fig. 11.6.
TRENDS AND TREND REVERSALS
Trend is the direction of movement of share prices in the market. When the
prices move upwards, it is a rising trend or uptrend. When the prices move
downwards, we have a falling trend or downtrend. We have a flat trend
when the prices move within a narrow range.
Share prices seldom move in a straight line. The main trend is interrupted by
short-term counter movements known as secondary reactions. The result is a
zig-zag movement giving rise to alternating tops and bottoms. The formation
of higher bottoms and higher tops indicates a rising trend, while the
formation of lower tops and lower bottoms indicates a falling trend.
The change in the direction of trend is referred to as trend reversal. A share
that exhibits a rising trend may start to move narrowly or fall after sometime.
This change in the direction of movement represents a trend reversal. The
reversal from a rising trend to a falling trend is marked by the formation of a
lower top and a lower bottom. In the same way, the reversal from a falling
trend to a rising trend is characterised by the formation of a higher bottom
and a higher top.
A technical analyst tries to identify the trend reversals at an early stage so as
to trade profitably in the market. When the trend reverses and begins to rise
the technical analyst would recommend purchase of the share. When the
trend begins to fall, sale is indicated. During a flat trend the investor should
stay away from the market.
CHART PATTERNS
When the price bar charts of several days are drawn close together, certain
patterns emerge. These patterns are used by the technical analysts to identify
trend reversal and predict the future movement of prices. The chart patterns
may be classified as support and resistance patterns, reversal patterns and
continuation patterns.
Support and Resistance
Support and resistance are price levels at which the downtrend or uptrend in
price movements is reversed. Support occurs when price is falling but
bounces back or reverses direction every time it reaches a particular level.
When all these low points are connected by a horizontal line, it forms the
support line. In other words, support level is the price level at which
sufficient buying pressure is exerted to halt the fall in prices.
Resistance occurs when the share price moves upwards. The price may fall
back every time it reaches a particular level. A horizontal line joining these
tops forms the resistance level. Thus, resistance level is the price level where
sufficient selling pressure is exerted to halt the ongoing rise in the price of a
share.
Figure 11.7 illustrates support and resistance levels.
If the scrip were to break the support level and move downwards, it has
bearish implications signalling the possibility of a further fall in prices.
Similarly, if the scrip were to penetrate the resistance level it would be
indicative of a bullish trend or a further rise in prices.
Once a support level is violated, it would reverse roles and become a
resistance level for any future upward movement in price. Similarly,
resistance level which is violated becomes the new support level for any
future downward movement in price.
Reversal Patterns
Price movements exhibit uptrends and downtrends. The trends reverse
direction after a period of time. These reversals can be identified with the
help of certain chart formations that typically occur during these trend
reversals. Thus, reversal patterns are chart formations that tend to signal a
change in direction of the earlier trend.
Head and Shoulder Formation
The most popular reversal pattern is the Head and Shoulder formation which
usually occurs at the end of a long uptrend. This formation exhibits a hump or
top followed by a still higher top or peak and then another hump or lower top.
This formation resembles the head and two shoulders of a man and hence the
name head and shoulder formation.
The first hump, known as the left shoulder, is formed when the prices reach
the top under a strong buying impulse. Then trading volume becomes less
and there is a short downward swing. This is followed by another high
volume advance, which takes the price to a higher top known as the head.
This is followed by another reaction on less volume which takes the price
down to a bottom near to the earlier downswing. A third rally now occurs
taking the price to a height less than the head but comparable to the left
shoulder. This rally results in the formation of the right shoulder. A
horizontal line joining the bottoms of this formation is known as the
neckline. As the price penetrates this neckline, the formation of the head and
shoulder pattern is completed. Figure 11.8 shows a head and shoulder
formation.
The head and shoulder formation usually occurs at the end of a bull phase
and is indicative of a reversal of trend. After breaking the neckline, the price
is expected to decline sharply.
Inverse Head and Shoulder Formation
This pattern is the reverse of the head and shoulder formation described
above and is really an inverted head and shoulder pattern. This occurs at the
end of a bear phase and consists of three distinct bottoms. The first bottom is
the left shoulder, then comes a lower bottom which forms the head,
followed by a third bottom which is termed the right shoulder. The neckline
is drawn by joining the tops from which the head and the right shoulder
originate. When the price rises above the neckline the formation of the
pattern is considered to be completed. An inverse head and shoulder
formation is shown in Fig. 11.9.
The inverse head and shoulder pattern is also a reversal pattern indicative of
an oncoming bullish phase. In the formation of this pattern a large increase in
volume becomes necessary.
Double top formation, triple top formation, double bottom formation, triple
bottom formation, etc. are some of the other reversal patterns.
Continuation Patterns
There are certain patterns which tend to provide a breathing space to the
earlier sharp rise or fall and after the completion of these patterns, the price
tends to move along the original trend. These patterns are formed during side
way movements of share prices and are called continuation patterns
because they indicate a continuation of the trend prevailing before the
formation of the pattern.
Triangles
Triangles are the most popular among the continuation patterns. Triangles are
formed when the price movements result in two or more consecutive
descending tops and two or more consecutive ascending bottoms. The
triangle becomes apparent on the chart when the consecutive tops are joined
by a straight line and the consecutive bottoms are joined by another straight
line. The two straight lines are the upper trend line and the lower trend line
respectively. A triangle is illustrated in Fig. 11.10.
The triangle formation may occur during a bull phase or a bear phase. In
either case it would indicate a continuation of the trend. It is generally seen
that the volume diminishes during the movement within the triangular
pattern. The breakout from the pattern is usually accompanied by increasing
volume.
Flags and Pennants
These are considered to be very reliable continuation patterns. They represent
a brief pause in a fast moving market. They occur mid-way between a sharp
rise in price or a steep fall in price.
The flag formation looks like a parallelogram with the two trend lines
forming two parallel lines. The volume of trading is expected to fall during
the formation of the flag and again pick up on breaking out from the pattern.
Figure 11.11 illustrates the flag formation.
The pennant formation looks like a symmetrical triangle. The upper trendline
formed by connecting the tops stoops downwards, whereas the lower
trendline formed by connecting the bottoms rises upwards. A pennant
formation is illustrated in Fig. 11.12.
The pennant is formed midway between either a bullish trend or a bearish
trend and signals the continuation of the same trend. The break out from the
pattern is marked by increased volume of trading.
ELLIOT WAVE THEORY
There are many theories which seek to explain the behaviour of the stock
market. One such theory, in technical analysis, is the Wave theory formulated
by Ralph Elliot, known as the Elliot wave theory.
The theory was formulated in 1934 by Elliot after analysing seventy five
years of stock price movements and charts. From his studies he concluded
that the market movement was quite orderly and followed a pattern of waves.
A wave is a movement of the market price from one change in the direction
to the next change in the same direction. The waves are the result of buying
and selling impulses emerging from the demand and supply pressures on the
market. Depending on the demand and supply pressures, waves are generated
in the prices.
According to this theory, the market moves in waves. A movement in a
particular direction can be represented by five distinct waves. Of these five
waves, three waves are in the direction of the movement and are termed as
impulse waves. Two waves are against the direction of the movement and
are termed as corrective waves or reaction waves. Waves 1, 3 and 5 are the
impulse waves and waves 2 and 4 are the corrective waves. Figure 11.13
illustrates the wave theory of Elliot.
The wave 1 is upwards and wave 2 corrects the wave 1. Similarly, waves 3
and 5 are those with an upward impulse and wave 4 corrects wave 3.
Corrections involve correcting the earlier rise. Thus, wave 2 would correct
the rise of wave 1; wave 4 would correct the rise of wave 3 and after the
completion of wave 5, there would come a correction which would be
labelled ABC. This correction would be in three waves in which waves A and
C will be against the trend and wave B will be along the trend. This ABC
correction following the fifth wave would correct the entire rise from the start
of wave 1 to the end of the fifth wave. It would be greater in dimension than
either the second or fourth corrective wave.
One complete cycle consists of waves made up of two distinct phases, bullish
and bearish. Once the full cycle of waves is completed after the termination
of the 8 wave movement, there will be a fresh cycle starting with similar
impulses arising out of market trading.
The Elliot wave theory is based on the principle that action is followed by
reaction. Although the wave theory is not perfect and there are many
limitations in its practical use, it is accepted as one of the tools of technical
analysis. The theory is used for predicting the future price changes and in
deciding the timing of investment.
MATHEMATICAL INDICATORS
Share prices do not rise or fall in straight lines. The movements are erratic.
This makes it difficult for the analyst to gauge the underlying trend. He can
use the mathematical tool of moving averages to smoothen out the apparent
erratic movements of share prices and highlight the underlying trend.
Moving Averages
Moving averages are mathematical indicators of the underlying trend of the
price movement. Two types of moving averages (MA) are commonly used
by analysts—the simple moving average and the exponential moving
average. The closing prices of shares are generally used for the calculation of
moving averages.
Simple Moving Average
An average is the sum of prices of a share for a specific number of days
divided by the number of days. In a simple moving average, a set of averages
are calculated for a specific number of days, each average being calculated by
including a new price and excluding an old price.
The calculation of a simple moving average is illustrated below:
Calculation of Five-day Simple MA
Days
Closing prices
Total of prices of 5 days
Five day MA
(1)
(2)
(3)
(4)
1
33
−
−
2
35
−
−
3
37.5
−
−
4
36
−
−
5
39
180.5
36.1
6
40
187.5
37.5
7
40.5
193.0
38.6
8
38.5
194.0
38.8
9
41
198.0
39.6
10
42
202.0
40.4
11
44
206.0
41.2
12
42.5
208.0
41.6
13
42
211.5
42.3
14
44
214.5
42.9
15
45
217.5
43.5
The first total of 180.5 in column 3 is obtained by adding the prices of the
first five days, that is, (33 + 35 + 37.5 + 36 + 39). The second total of 187.5
in column 3 is obtained by adding the price of the 6th day and deleting the
price of the first day from the first total, that is, (180.5 + 40 − 33). This
process is continued. The moving average in column 4 is obtained by
dividing the total figure in column 3 by the number of days, namely 5.
Exponential Moving Average
Exponential moving average (EMA) is calculated by using the following
formula:
and n = number of days for which the average is to be calculated.
The calculation of exponential moving average is illustrated below.
The EMA for the first day is taken as the closing price of that day itself. The
EMA for the second day is calculated as shown below.
EMA = (Closing price − Previous EMA) × Factor + Previous EMA
= (35 − 33) × 0.33 + 33 = 33.66
EMA for the third day = (37.5 − 33.66) × 0.33 + 33.66 = 34.93
If we are calculating the five day exponential moving average, the correct
five day EMA will be available from the sixth day onwards.
A moving average represents the underlying trend in the share price
movement. The period of the average indicates the type of trend being
identified. For example, a five day or ten day average would indicate the
short-term trend; a 50 day average would indicate the medium-term trend and
a 200 day average would represent the long-term trend.
The moving averages are plotted on the price charts. The curved line joining
these moving averages represent the trend line. When the price of the share
intersects and moves above or below this trendline, it may be taken as the
first sign of trend reversal.
Sometimes, two moving averages—one short-term and the other long-term—
are used in combination. In this case, trend reversal is indicated by the
intersection of the two moving averages.
Oscillators
Oscillators are mathematical indicators calculated with the help of the closing
price data. They help to identify overbought and oversold conditions and also
the possibility of trend reversals. These indicators are called oscillators
because they move across a reference point.
Rate of Change Indicator (ROC)
It is a very popular oscillator which measures the rate of change of the current
price as compared to the price a certain number of days or weeks back. To
calculate a 7 day rate of change, each day’s price is divided by the price
which prevailed 7 days ago and then 1 is subtracted from this price ratio.
The calculation of ROC is illustrated below:
Calculation of 7 Day ROC
Days
Closing price
Closing price 7 days ago
Price ratio
ROC = Ratio − 1
1
70
−
−
−
2
72
−
−
−
3
73
−
−
−
4
70
−
−
−
5
74
−
−
−
6
76
−
−
−
7
77
−
−
−
8
75
70
1.07
0.07
9
78
72
1.08
0.08
10
80
73
1.10
0.10
11
79
70
1.13
0.13
12
78
74
1.05
0.05
13
76
76
1.00
0.00
14
75
77
0.97
− 0.03
15
77
75
1.03
0.03
16
78
78
1.00
0.00
17
76
80
0.95
− 0.05
18
75
79
0.95
− 0.05
The ROC values may be positive, negative or zero. An ROC chart is shown
in Fig. 11.14 where the X axis represents the time and the Y axis represents
the values of the ROC. The ROC values oscillate across the zero line. When
the ROC line is above the zero line, the price is rising and when it is below
the zero line, the price is falling.
Ideally, one should buy a share that is oversold and sell a share that is
overbought. In the ROC chart, the overbought zone is above the zero line and
the oversold zone is below the zero line. Many analysts use the zero line for
identifying buying and selling opportunities. Upside crossing (from below to
above the zero line) indicates a buying opportunity, while a downside
crossing (from above to below the zero line) indicates a selling opportunity.
The ROC has to be used along with the price chart. The buying and selling
signals indicated by the ROC should also be confirmed by the price chart.
Relative Strength Index (RSI)
This is a powerful indicator that signals buying and selling opportunities
ahead of the market. RSI for a share is calculated by using the following
formula.
The most commonly used time period for the calculation of RSI is 14 days.
For the calculation a 14 day RSI, the gain per day or loss per day is arrived at
by comparing the closing price of a day with that of the previous day for a
period of 14 days. The gains are added up and divided by 14 to get the
average gain per day. Similarly, the losses are added up and divided by 14 to
get the average loss per day. The average gain per day and the average loss
per day are used in the above formula for calculating the RSI for a day. In
this way RSI values can be calculated for a number of days.
The calculation of RSI is illustrated below.
This is the RSI for day 15. In this way the RSI values for the subsequent days
can be calculated by taking the closing prices of 14 previous days. The RSI
values range from 0 to 100. These values are then plotted on an XY graph as
shown below in Fig. 11.15.
RSI values above 70 are considered to denote overbought condition and
values below 30 are considered to denote oversold condition. When the RSI
has crossed the 30 line from below to above and is rising, a buying
opportunity is indicated. When it has crossed the 70 line from above to below
and is falling, a sell signal is indicated.
Moving Average Convergence and Divergence (MACD)
MACD is an oscillator that measures the convergence and divergence
between two exponential moving averages. A short-term exponential moving
average and a long-term exponential moving average are calculated with the
help of the closing price data. A 12-day and 48-day exponential moving
averages constitute a popular combination. The difference between the shortterm EMA and the long-term EMA represents MACD.
The MACD values for different days are derived by deducting the long-term
EMA for each day from the corresponding short-term EMA for the day.
These MACD values are plotted on an XY graph with MACD values on the Y
axis and time periods on X axis. The MACD line would oscillate across the
zero line. If the MACD line crosses the zero line from above, the trend can be
considered to have turned bearish, signalling a selling opportunity. On the
other hand, if the MACD line moves above the zero line from below, the
trend can be said to have turned bullish and indicates a buying opportunity.
Sometimes, a simple moving average or an exponential moving average of
the MACD values is superimposed over the MACD graph. Then buy and sell
signals are generated by the cross over of the average line and the MACD
line. When the lines are below the zero line, if the MACD line crosses the
average line from below to above, it indicates a buying opportunity. When
the lines are above the zero line, crossing of the MACD line from above to
below the average line signals a selling opportunity.
MARKET INDICATORS
Technical analysis focuses its attention not only on individual stock price
behaviour, but also on the general trend of the market. Indicators used by
technical analysts to study the trend of the market as a whole are known as
market indicators. Some of these indicators are discussed below.
Breadth of the Market
By comparing the number of shares which advanced and the number of
shares that declined during a period, the trend of the market can be
ascertained. Comparison of advances and declines is a means of measuring
the dispersion or breadth of a general price rise or decline. The difference
between the advances and declines is called the breadth of the market.
The breadth is calculated by taking the daily net difference between the
number of shares that have advanced and the number of shares that have
declined. Each day’s difference is added to the next day’s difference to form
a continuous cumulative index as shown in the table below.
Calculation of Breadth
Day
Advances
Declines
Daily
Breadth (Cumulative difference)
difference
Monday
620
350
+270
+270
Tuesday
470
510
−40
+230
Wednesday
360
610
−250
−20
Thursday
585
380
+205
+185
Friday
705
270
+435
+620
The index is plotted as a line graph and compared with the market index.
Normally, breadth and market index move in unison. When they diverge, a
key signal occurs. In case of divergence, the breadth line shows the true
direction of the market. For instance, during a bull market if breadth declines
to new lows while the market index makes new highs a peak is suggested
followed by a downturn in stock prices. Breadth may also signal recovery.
This happens when the breadth line begins to rise even as the market index is
reaching new lows.
Short Interest
A speculator often resorts to short selling which is selling a share that is not
owned by the person. This is done when the speculator feels that the price of
the stock will fall in future. He hopes to purchase the share at a later date
(cover his short position) below the selling price and reap a profit.
The volume of short sales in the market can be used as a market indicator. As
a technical indicator, short selling is called short interest. The expectation is
that short sellers must eventually cover their positions. This buying activity
increases the demand for stocks. Thus, short interest has significance for the
market as a whole.
Monthly short selling volume is related to the average daily volume for the
preceding month. Thus, monthly short selling volume is divided by average
daily volume to give a ratio which indicates how many days of trading it
would take to cover up the total short sales.
In general, when the ratio is less than 1.0, the market is considered to be
weakening or ‘overbought’. A decline should follow sooner or later. Values
above 1.5 are considered to indicate that the market is ‘oversold’ and is likely
to turn bullish shortly.
Odd-lot Index
Small investors are presumed to buy smaller number of shares than the
normal trading lot of 100 shares. These are known as odd lots and the buyers
and sellers of odd lots are called odd lotters. Technical analysts believe that
the odd lotters are inclined to do the wrong thing at critical turns in the
market because of their presumed lack of sophistication.
An odd-lot index can be calculated by relating odd-lot purchases to odd-lot
sales. The odd-lot index is obtained by dividing odd-lot purchases by odd-lot
sales. An increase in this index suggests relatively more buying activity and
vice versa. At or near the peak of a bull market, when the investors should be
selling their shares, the odd lotters would be buying proportionately more
than selling. Thus, the odd-lot index rises noticeably just before a decline in
the market. Similarly, the odd-lot sales increase greatly causing a fall in the
odd-lot index just before a rise in the market.
Mutual Fund Cash Ratio
Mutual funds represent one of the most important institutional forces in the
market. Mutual fund cash as a percentage of their net assets on a daily or
weekly or monthly basis has been a popular market indicator. Mutual funds
keep cash to take advantage of favourable market opportunities and to
provide for redemption of their units by holders. The theory is that a low cash
ratio of, say about five per cent, would indicate a reasonably fully invested
position leaving negligible buying power in their hands. Low cash ratios are
equated with market highs indicating that the market is about to decline. At
market bottoms the cash ratio would be high. This is an indication of
potential purchasing power which can propel a rise in prices. Thus, high
mutual fund cash ratio signals a rise in prices of shares.
A few other market indicators are also being used by technical analysts to
predict changes in the direction of the overall market.
Technical Analysis vs Fundamental Analysis
Fundamental analysis tries to estimate the intrinsic value of a security by
evaluating the fundamental factors affecting the economy, industry and
company. This is a tedious process and takes a rather long time to complete
the process.
Technical analysis studies the price and volume movements in the market and
by carefully examining the pattern of these movements, the future price of the
stock is predicted. Since the whole process involves much less time and data
analysis, compared to fundamental analysis, it facilitates timely decision.
Fundamental analysis helps in identifying undervalued or overvalued
securities. But technical analysis helps in identifying the best timing of an
investment, i.e. the best time to buy or sell a security identified by
fundamental analysis as undervalued or overvalued. Thus, technical analysis
may be used as a supplement to fundamental analysis rather than as a
substitute to it. The two approaches, however, differ in terms of their
databases and tools of analysis. Fundamental analysis and technical analysis
are two alternative approaches to predicting stock price behaviour. Neither of
them is perfect nor complete by itself.
Technical analysis has several limitations. It is not an accurate method of
analysis. It is often difficult to identify the patterns underlying stock price
movements. Moreover, it is not easy to interpret the meaning of patterns and
their likely impact on future price movements.
REVIEW QUESTIONS
1. What is technical analysis?
2. Explain the basic principles and hypotheses of Dow theory.
3. Describe the formation of bullish trend and bearish trend in the market.
4. What are price charts? Describe the different types of price charts used
by technical analysts.
5. Describe the chart patterns that help to identify trend reversal.
6. “The Elliot Wave Theory is based on the principle that action is
followed by reaction.” Elucidate.
7. How are moving averages useful in studying trends and trend reversals?
8. Write short notes on:
(a) Japanese candlestick charts
(b) Trend reversal
(c) Support and resistance patterns
(d) Flags and pennants
(e) Exponential moving average
(f) MACD
9. What are oscillators? Explain the calculation and interpretation of any
one oscillator.
10. What is RSI? Explain its calculation and interpretation.
11. Describe the important market indicators that are useful in studying the
trend of the market.
12. Explain the merits and demerits of technical analysis as a tool of
security analysis.
12
EFFICIENT MARKET THEORY
Stock prices are determined by a number of factors such as fundamental
factors, technical factors and psychological factors. The behaviour of stock
prices is studied with the help of different methods such as fundamental
analysis and technical analysis. Fundamental analysis seeks to evaluate the
intrinsic value of securities by studying the fundamental factors affecting the
performance of the economy, industry and companies. Technical analysis
believes that the past behaviour of stock prices gives an indication of the
future behaviour. It tries to study the patterns in stock price behaviour
through charts and predict the future movement in prices. There is a third
theory on stock price behaviour which questions the assumptions of technical
analysis.
The basic assumption in technical analysis is that stock price movement is
quite orderly and not random. The new theory questions this assumption.
From the results of several empirical studies on stock price movements, the
advocates of the new theory assert that share price movements are random.
The new theory came to be known as Random Walk Theory because of its
principal contention that share price movements represent a random walk
rather than an orderly movement.
RANDOM WALK THEORY
Stock price behaviour is explained by the theory in the following manner. A
change occurs in the price of a stock only because of certain changes in the
economy, industry or company. Information about these changes alters the
stock prices immediately and the stock moves to a new level, either upwards
or downwards, depending on the type of information. This rapid shift to a
new equilibrium level whenever new information is received, is a recognition
of the fact that all information which is known is fully reflected in the price
of the stock. Further change in the price of the stock will occur only as a
result of some other new piece of information which was not available
earlier. Thus, according to this theory, changes in stock prices show
independent behaviour and are dependent on the new pieces of information
that are received but within themselves are independent of each other. Each
price change is independent of other price changes because each change is
caused by a new piece of information.
The basic premise in random walk theory is that the information on changes
in the economy, industry and company performance is immediately and fully
spread so that all investors have full knowledge of the information. There is
an instant adjustment in stock prices either upwards or downwards. Thus, the
current stock price fully reflects all available information on the stock.
Therefore, the price of a security two days ago can in no way help in
speculating the price two days later. The price of each day is independent. It
may be unchanged, higher or lower from the previous price, but that depends
on new pieces of information being received each day.
The random walk theory presupposes that the stock markets are so efficient
and competitive that there is immediate price adjustment. This is the result of
good communication system through which information can be spread almost
anywhere in the country instantaneously. Thus, the random walk theory is
based on the hypothesis that the stock markets are efficient. Hence, this
theory later came to be known as the efficient market hypothesis (EMH) or
the efficient market model.
THE EFFICIENT MARKET HYPOTHESIS
This hypothesis states that the capital market is efficient in processing
information. An efficient capital market is one in which security prices equal
their intrinsic values at all times, and where most securities are correctly
priced. The concept of an efficient capital market has been one of the
dominant themes in academic literature since the 1960s. According to Elton
and Gruber, “when someone refers to efficient capital markets, they mean
that security prices fully reflect all available information”.1 According to
Eugene Fama,2 in an efficient market, prices fully reflect all available
information. The prices of securities observed at any time are based on
correct evaluation of all information available at that time.
The efficient market model is actually concerned with the speed with which
information is incorporated into security prices. The technicians believe that
past price sequence contains information about the future price movements
because they believe that information is slowly incorporated in security
prices. This gives technicians an opportunity to earn excess returns by
studying the patterns in price movements and trading accordingly.
Fundamentalists believe that it may take several days or weeks before
investors can fully assess the impact of new information. As a consequence,
the price may be volatile for a number of days before it adjusts to a new level.
This provides an opportunity to the analyst who has superior analytical skills
to earn excess returns.
The efficient market theory holds the view that in an efficient market, new
information is processed and evaluated as it arrives and prices
instantaneously adjust to new and correct levels. Consequently, an investor
cannot consistently earn excess returns by undertaking fundamental analysis
or technical analysis.
FORMS OF MARKET EFFICIENCY
The capital market is considered to be efficient in three different forms: the
weak form, semi-strong form and the strong form. Thus, the efficient market
hypothesis has been subdivided into three forms, each dealing with a
different type of information. The weak form deals with the information
regarding the past sequence of security price movements, the semi-strong
form deals with the publicly available information, while the strong form
deals with all information, both public and private (or inside).
The different forms of efficient market hypothesis have been tested through
several empirical studies. The tests of the weak form hypothesis are
essentially tests of whether all information contained in historical prices of
securities is fully reflected in current prices. Semi-strong form tests of the
efficient market hypothesis are tests of whether publicly available
information is fully reflected in current stock prices. Finally, strong form tests
of the efficient market hypothesis are tests of whether all information, both
public and private (or inside), is fully reflected in security prices and whether
any type of investor is able to earn excess returns.
Empirical Tests of Weak Form Efficiency
The weak form of the efficient market hypothesis (EMH) says that the current
prices of stocks already fully reflect all the information that is contained in
the historical sequence of prices. The new price movements are completely
random. They are produced by new pieces of information and are not related
or dependent on past price movements. Therefore, there is no benefit in
studying the historical sequence of prices to gain abnormal returns from
trading in securities. This implies that technical analysis, which relies on
charts of price movements in the past, is not a meaningful analysis for
making abnormal trading profits.
The weak form of the efficient market hypothesis is thus a direct repudiation
of technical analysis.
Two approaches have been used to test the weak form of the efficient market
hypothesis. One approach looks for statistically significant patterns in
security price changes. The alternative approach searches for profitable short-
term trading rules.
Serial Correlation Test
Since the weak form EMH postulates independence between successive price
changes, such independence or randomness in stock price movements can be
tested by calculating the correlation between price changes in one period and
changes for the same stock in another period. The correlation coefficient can
take on a value ranging from −1 to 1; a positive number indicates a direct
relation, a negative value implies an inverse relationship and a value close to
zero implies no relationship. Thus, if correlation coefficient is close to zero,
the price changes can be considered to be serially independent.
Run Test
The run test is another test used to test the randomness in stock price
movements. In this test, the absolute values of price changes are ignored,
only the direction of change is considered. An increase in price is represented
by + sign. The decrease is represented by − sign. When there is no change in
prices, it is represented by ‘0’. A consecutive sequence of the same sign is
considered as a run. For example, the sequence + + + − − − has two runs. In
other words, a change of sign indicates a new run. The sequence − − − + + 0
− − − + + + + has five runs; a run of three − ’s, followed by a run of two + ’s,
another run of one 0, a fourth run of three − ’s and a fifth run of four + ’s. In a
run test, the actual number of runs observed in a series of stock price
movements is compared with the number of runs in a randomly generated
number series. If no significant differences are found, then the security price
changes are considered to be random in nature.
Filter Tests
If stock price changes are random in nature, it would be extremely difficult to
develop successful mechanical trading systems. Filter tests have been
developed as direct tests of specific mechanical trading strategies to examine
their validity and usefulness.
It is often believed that, as long as no new information enters the market, the
price fluctuates randomly within two barriers—one lower, and the other
higher—around the fair price. When new information comes into the market,
a new equilibrium price will be determined. If the news is favourable, then
the price should move up to a new equilibrium above the old price. Investors
will know that this is occurring when the price breaks through the old barrier.
If investors purchase at this point, they will benefit from the price increase to
the new equilibrium level.
Likewise, if the news received is unfavourable, the price of the stock will
decline to a lower equilibrium level. If investors sell the stock as it breaks the
lower barrier, they will avoid much of the decline. Technicians set up trading
strategies based on such patterns to earn excess returns. The strategy is called
a filter rule. The filter rule is usually stated in the following way: Purchase
the stock when it rises by x per cent from the previous low and sell it when it
declines by x per cent from the subsequent high. The filters may range from 1
per cent to 50 per cent or more. The alternative to this active trading strategy
is the passive buy and hold strategy.
The returns generated by trading according to the filter rule are compared
with the returns earned by an investor following the buy and hold strategy. If
trading with filters results in superior returns that would suggest the existence
of patterns in price movements and negate the weak form EMH.
Distribution Pattern
It is a rule of statistics that the distribution of random occurrences will
conform to a normal distribution. Then, if price changes are random, their
distribution should also be approximately normal. Therefore, the distribution
of price changes can be studied to test the randomness or otherwise of stock
price movements.
In the 1960s the efficient market theory was known as the random walk
theory. The empirical studies regarding share price movements were testing
whether prices followed a random walk.
Two articles by Roberts and Osborne, both published in 1959, stimulated a
great deal of discussion of the new theory then called random walk theory.
Roberts’ study compared the movements in the Dow Jones Industrial
Average (an American stock market index) with the movement of a variable
generated from a random walk process. He found that the random walk
process produced patterns which were very similar to those of the Dow Jones
index.
Osborne’s study found a close resemblance between share price changes and
the random movement of small particles suspended in a solution, which is
known in Physics as the Brownian motion. Both the studies suggested that
share price changes are random in nature and that past prices had no
predictive value.
During the 1960s there was an enormous growth in serial correlation testing.
None of these found any substantial linear dependence in price changes.
Studies by Moore, Fama and Hagerman and Richmond are some of the early
studies in this area. Moore found an average serial correlation coefficient of −
0.06 for price changes measured over weekly intervals. Fama’s study tested
the serial correlation for the thirty stocks comprising the Dow Jones industrial
average for the five years prior to 1962. The average serial correlation
coefficient was found to be 0.03. Both the coefficients were not statistically
different from zero; thus both the studies supported the random walk theory.
Fama also used run tests to measure dependency. The results again supported
the random walk theory. Many studies followed Moore’s and Fama’s work
each of which used different databases. The results of these studies were
much the same as those of Moore and Fama.
Hagerman and Richmond conducted similar studies on securities traded in
the ‘over-the-counter’ market and found little serial correlation. Serial
correlation tests of dependence have also been carried out in various other
stock markets around the world. These have similarly revealed little or no
serial correlation.
Much research has also been directed towards testing whether mechanical
trading strategies are able to earn above average returns. Many studies have
tested the filter rules for its ability to earn superior returns. Early American
studies were those by Alexander, who originally advocated the filter strategy,
and by Fama and Blume. There were similar studies in the United Kingdom
by Dryden and in Australia by Praetz. All these studies have found that filter
strategies did not achieve above average returns. Thus, the results of
empirical studies have been virtually unanimous in finding little or no
statistical dependence and price patterns and this has corroborated the weak
form efficient market hypothesis.
Empirical Tests of Semi-strong Form Efficiency
The semi-strong form of the efficient market hypothesis says that current
prices of stocks not only reflect all informational content of historical prices,
but also reflect all publicly available information about the company being
studied. Examples of publicly available information are—corporate annual
reports, company announcements, press releases, announcements of
forthcoming dividends, stock splits, etc. The semi-strong hypothesis
maintains that as soon as the information becomes public the stock prices
change and absorb the full information. In other words, stock prices
instantaneously adjust to the information that is received.
The implication of semi-strong hypothesis is that fundamental analysts
cannot make superior gains by undertaking fundamental analysis because
stock prices adjust to new pieces of information as soon as they are received.
There is no time gap in which a fundamental analyst can trade for superior
gains. Thus, the semi-strong hypothesis repudiates fundamental analysis.
Semi-strong form tests deal with whether or not security prices fully reflect
all publicly available information. These tests attempt to establish whether
share prices react precisely and quickly to new items of information. If prices
do not react quickly and adequately, then an opportunity exists for investors
or analysts to earn excess returns by using this information. Therefore, these
tests also attempt to find if analysts are able to earn superior returns by using
publicly available information.
There is an enormous amount and variety of public information. Semi-strong
form tests have been performed with respect to many different types of
information. Much of the methodology used in semi-strong form tests has
been introduced by Fama, Fisher, Jensen and Roll. Theirs was the first of the
studies that were directly concerned with the testing of the semi-strong form
of EMH. Subsequent to their study, a number of refinements have been
developed in the test procedure.
The general methodology followed in these studies has been to take an
economic event and measure its impact on the share price. The impact is
measured by taking the difference between the actual return and expected
return on a security. The expected return on a security is generally estimated
by using the market model (or single index model) suggested by William
Sharpe. The model used for estimating expected returns is the following:
Ri = ai + bi Rm + ei
where
Ri = Return on security i.
Rm = Return on a market index.
ai and bi = Constants.
ei = Random error.
This analysis is known as Residual analysis. The positive difference between
the actual return and the expected return represents the excess return earned
on a security. If the excess return is close to zero, it implies that the price
reaction following the public announcement of an information is immediate
and the price adjusts to a new level almost immediately. Thus, the lack of
excess returns would validate the semi-strong form EMH.
Major studies on the impact of capitalisation issues such as stock splits and
stock dividends have been conducted in the United States by Fama, Fisher,
Jensen and Roll and Johnson, in Canada by Finn, and in the United Kingdom
by Firth. All these studies found that the market adjusted share prices
instantaneously and accurately for the new information. Both Pettit and Watts
have investigated the market’s reaction to dividend announcements. They
both found that all the price adjustment was over immediately after the
announcement and thus, the market had acted quickly in evaluating the
information.
Other items of information whose impact on share prices have been tested
include announcements of purchase and sale of large blocks of shares of a
company, takeovers, annual earnings of companies, quarterly earnings,
accounting procedure changes, and earnings estimates made by company
officials. All these studies which made use of the Residual analysis
approach, showed the market to be relatively efficient.
Ball and Brown tested the stock market’s ability to absorb the informational
content of reported annual earnings per share information. They found that
companies with good earnings report experienced price increase in stock,
while companies with bad earnings report experienced decline in stock
prices. But surprisingly, about 85 per cent of the informational content of the
earnings announcements was reflected in stock price movements prior to the
release of the actual earnings figure. The market seems to adjust to new
information rapidly with much of the impact taking place in anticipation of
the announcement.
Joy, Litzenberger and McEnally tested the impact of quarterly earnings
announcements on the stock price adjustment mechanism. Some of their
results, however, contradicted the semi-strong form of the efficient market
hypothesis. They found that the favourable information contained in
published quarterly earnings reports was not always instantaneously adjusted
in stock prices. This may suggest that the market does not adjust share prices
equally well for all types of information.
By way of summary it may be stated that a great majority of the semi- strong
efficiency tests provide strong empirical support for the hypothesis; however,
there have been some contradictory results too. Most of the reported results
show that stock prices do adjust rapidly to announcements of new
information and that investors are typically unable to utilise this information
to earn consistently above average returns.
Tests of Strong Form Efficiency
The strong form hypothesis represents the extreme case of market efficiency.
The strong form of the efficient market hypothesis maintains that the current
security prices reflect all information both publicly available information as
well as private or inside information. This implies that no information,
whether public or inside, can be used to earn superior returns consistently.
The directors of companies and other persons occupying senior management
positions within companies have access to much information that is not
available to the general public. This is known as inside information. Mutual
funds and other professional analysts who have large research facilities may
gather much private information regarding different stocks on their own.
These are private information not available to the investing public at large.
The strong form efficiency tests involve two types of tests. The first type of
tests attempt to find whether those who have access to inside information
have been able to utilise profitably such inside information to earn excess
returns. The second type of tests examine the performance of mutual funds
and the recommendations of investment analysts to see if these have
succeeded in achieving superior returns with the use of private information
generated by them.
Jaffe, Lorie and Niederhoffer studied the profitability of insider trading (i.e.
the investment activities of people who had inside information on
companies). They found that insiders earned returns in excess of expected
returns. Although there have been only a few empirical studies on the
profitability of using inside information, the results show, as expected, that
excess returns can be made. These results indicate that markets are probably
not efficient in the strong form.
Many studies have been carried out regarding the performance of American
mutual funds using fairly sophisticated evaluation models. All the major
studies have found that mutual funds did no better than randomly constructed
portfolios of similar risk. Firth studied the performance of Unit Trusts in the
United Kingdom during the period 1965−75. He also found that unit trusts
did not outperform the market index for their given levels of risk. A small
research has been conducted into the profitability of investment
recommendations by investment analysts. Such studies suggest that few
analysts or firms of advisers can claim above average success with their
forecasts.
The results of research on strong form EMH may be summarised as follows:
1. Inside information can be used to earn above average returns.
2. Mutual funds and investment analysts have not been able to earn
superior returns by using their private information.
In conclusion, it may be stated that the strong form hypothesis is invalid as
regards inside information, but valid as regards private information other than
inside information.
EMH vs FUNDAMENTAL AND TECHNICAL ANALYSES
There are three broad theories concerning stock price movements. These are
the fundamental analysis, technical analysis and efficient market
hypothesis. Fundamental analysts believe that by analysing key economic
and financial variables they can estimate the intrinsic worth of a security and
then determine what investment action to take. Fundamental analysis seeks to
identify underpriced securities and overpriced securities. Their investment
strategy consists in buying underpriced securities and selling overpriced
securities, thereby earning superior returns.
A technical analyst maintains that fundamental analysis is unnecessary. He
believes that history repeats itself. Hence, he tries to predict future
movements in share prices by studying the historical patterns in share price
movements.
The efficient market hypothesis is expressed in three forms. The weak form
of the EMH directly contradicts technical analysis by maintaining that past
prices and past price changes cannot be used to forecast future price changes
because successive price changes are independent of each other. The semistrong form of the EMH contradicts fundamental analysis to some extent by
claiming that the market is efficient in the dissemination and processing of
information and hence, publicly available information cannot be used
consistently to earn superior investment returns.
The strong form of the EMH maintains that not only is publicly available
information useless to the investor or analyst but all information is useless.
Even though the EMH repudiates both fundamental analysis and technical
analysis, the market is efficient precisely because of the organised and
systematic efforts of thousands of analysts undertaking fundamental and
technical analysis. Thus, the paradox of efficient market hypothesis is that
both fundamental and technical analysis are required to make the market
efficient and thereby validate the hypothesis.
COMPETITIVE MARKET HYPOTHESIS
An efficient market has been defined as one where share prices always fully
reflect available information on companies. In practice, no existing stock
market is perfectly efficient. There are evident shortcomings in the pricing
mechanism. Often, the complete body of knowledge about a company’s
prospects is not publicly available to market participants. Further, the
available information would not be always interpreted in a completely
accurate fashion. The research studies on EMH have shown that price
changes are random or independent and hence unpredictable. The prices are
also seen to adjust quickly to new information. Whether the price adjustments
are correct and accurate, reflecting correctly and accurately the meaning of
publicly available information, is difficult to determine.
All that can be validly concluded is that prices are set in a very competitive
market, but not necessarily in an efficient market. This competitive market
hypothesis provides scope for earning superior returns by undertaking
security analysis and following portfolio management strategies.
REVIEW QUESTIONS
1. What is Random Walk Theory?
2. “When someone refers to efficient capital markets, they mean that
security prices fully reflect all available information.” Discuss.
3. Explain the weak form of the efficient market hypothesis. Describe the
empirical tests used for testing the weak form efficiency.
4. What is the implication of semi-strong form market efficiency for
fundamental analysis?
5. Briefly describe the results of empirical tests of semi-strong form market
efficiency.
6. Write notes on:
(a) Serial correlation test
(b) Run test
(c) Filter tests
(d) Residual analysis
(e) Competitive market hypothesis
7. Explain the strong form of efficient market hypothesis. How far is it
validated?
8. Compare and contrast efficient market hypothesis with fundamental and
technical analyses.
9. “An investor cannot consistently earn excess returns by undertaking
fundamental analysis or technical analysis.” Discuss.
REFERENCES
1. Elton, Edwin J., and Martin J. Gruber, 1994, Modern Portfolio Theory
and Investment Analysis, 4th ed., p. 399, John Wiley & Sons, New York.
2. Fama, Eugene, 1970, “Efficient Capital Markets: A review of theory and
empirical work,” Journal of Finance, May.
13
PORTFOLIO ANALYSIS
Individual securities have risk return characteristics of their own. The future
return expected from a security is variable and this variability of returns is
termed risk. It is rare to find investors investing their entire wealth in a single
security. This is because most investors have an aversion to risk. It is hoped
that if money is invested in several securities simultaneously, the loss in one
will be compensated by the gain in others. Thus, holding more than one
security at a time is an attempt to spread and minimise risk by not putting all
our eggs in one basket.
Most investors thus tend to invest in a group of securities rather than a single
security. Such a group of securities held together as an investment is what is
known as a portfolio. The process of creating such a portfolio is called
diversification. It is an attempt to spread and minimise the risk in investment.
This is sought to be achieved by holding different types of securities across
different industry groups.
From a given set of securities, any number of portfolios can be constructed. A
rational investor attempts to find the most efficient of these portfolios. The
efficiency of each portfolio can be evaluated only in terms of the expected
return and risk of the portfolio as such. Thus, determining the expected return
and risk of different portfolios is a primary step in portfolio management.
This step is designated as portfolio analysis.
EXPECTED RETURN OF A PORTFOLIO
As a first step in portfolio analysis, an investor needs to specify the list of
securities eligible for selection or inclusion in the portfolio. Next he has to
generate the risk-return expectations for these securities. These are typically
expressed as the expected rate of return (mean) and the variance or standard
deviation of the return.
The expected return of a portfolio of assets is simply the weighted average of
the return of the individual securities held in the portfolio. The weight applied
to each return is the fraction of the portfolio invested in that security.
Let us consider a portfolio of two equity shares P and Q with expected
returns of 15 per cent and 20 per cent respectively.
If 40 per cent of the total funds is invested in share P and the remaining 60
per cent, in share Q, then the expected portfolio return will be:
(0.40 × 15) + (0.60 × 20) = 18 per cent
The formula for the calculation of expected portfolio return may be expressed
as shown below:
RISK OF A PORTFOLIO
The variance of return and standard deviation of return are alternative
statistical measures that are used for measuring risk in investment. These
statistics measure the extent to which returns are expected to vary around an
average over time. The calculation of variance of a portfolio is a little more
difficult than determining its expected return. The variance or standard
deviation of an individual security measures the riskiness of a security in
absolute sense. For calculating the risk of a portfolio of securities, the
riskiness of each security within the context of the overall portfolio has to be
considered. This depends on their interactive risk, i.e. how the returns of a
security move with the returns of other securities in the portfolio and
contribute to the overall risk of the portfolio.
Covariance is the statistical measure that indicates the interactive risk of a
security relative to others in a portfolio of securities. In other words, the way
security returns vary with each other affects the overall risk of the portfolio.
The covariance between two securities X and Y may be calculated using the
following formula:
The covariance is a measure of how returns of two securities move together.
If the returns of the two securities move in the same direction consistently the
covariance would be positive. If the returns of the two securities move in
opposite direction consistently the covariance would be negative. If the
movements of returns are independent of each other, covariance would be
close to zero.
Covariance is an absolute measure of interactive risk between two securities.
To facilitate comparison, covariance can be standardised. Dividing the
covariance between two securities by product of the standard deviation of
each security gives such a standardised measure. This measure is called the
coefficient of correlation. This may be expressed as:
The correlation coefficients may range from −1 to 1. A value of −1 indicates
perfect negative correlation between security returns, while a value of +1
indicates a perfect positive correlation. A value close to zero would indicate
that the returns are independent.
The variance (or risk) of a portfolio is not simply a weighted average of the
variances of the individual securities in the portfolio. The relationship
between each security in the portfolio with every other security as measured
by the covariance of return has also to be considered. The variance of a
portfolio with only two securities in it may be calculated with the following
formula.
Portfolio standard deviation can be obtained by taking the square root of
portfolio variance.
Let us take an example to understand the calculation of portfolio variance and
portfolio standard deviation. Two securities P and Q generate the following
sets of expected returns, standard deviations and correlation coefficient:
The standard deviation of the portfolio is:
= 17.09 per cent.
The return and risk of a portfolio depends on two sets of factors (a) the
returns and risks of individual securities and the covariance between
securities in the portfolio, (b) the proportion of investment in each security.
The first set of factors is parametric to the investor in the sense that he has no
control over the returns, risks and covariances of individual securities. The
second set of factors are choice variables in the sense that the investor can
choose the proportions of each security in the portfolio.
REDUCTION OF
DIVERSIFICATION
PORTFOLIO
RISK
THROUGH
The process of combining securities in a portfolio is known as
diversification. The aim of diversification is to reduce total risk without
sacrificing portfolio return. In the example considered above, diversification
has helped to reduce risk. The portfolio standard deviation of 17.09 is lower
than the standard deviation of either of the two securities taken separately,
which were 50 and 30 respectively.
To understand the mechanism and power of diversification, it is necessary to
consider the impact of covariance or correlation on portfolio risk more
closely. We shall examine three cases: (a) when security returns are perfectly
positively correlated, (b) when security returns are perfectly negatively
correlated, and (c) when security returns are not correlated.
Security Returns Perfectly Positively Correlated
When security returns are perfectly positively correlated the correlation
coefficient between the two securities will be +1. The returns of the two
securities then move up or down together.
The portfolio variance is calculated using the formula:
This is simply the weighted average of the standard deviations of the
individual securities.
Taking the same example that we considered earlier for calculating portfolio
variance, we shall calculate the portfolio standard deviation when correlation
coefficient is +1.
Standard deviation of security P = 50
Standard deviation of security Q = 30
Proportion of investment in P = 0.4
Proportion of investment in Q = 0.6
Correlation coefficient = +1.0
Portfolio standard deviation may be calculated as:
σp = x1σ1 + x2σ2
= (0.4) (50) + (0.6) (30)
= 38
Being the weighted average of the standard deviations of individual
securities, the portfolio standard deviation will lie between the standard
deviations of the two individual securities. In our example, it will vary
between 50 and 30 as the proportion of investment in each security changes.
For example, if the proportion of investment in P and Q are 0.75 and 0.25
respectively, portfolio standard deviation becomes:
σp = (0.75) (50) + (0.25) (30) = 45
Thus, when the security returns are perfectly positively correlated,
diversification provides only risk averaging and no risk reduction because the
portfolio risk cannot be reduced below the individual security risk. Hence,
diversification is not a productive activity when security returns are perfectly
positively correlated.
Security Returns Perfectly Negatively Correlated
When security returns are perfectly negatively correlated, the correlation
coefficient between them becomes −1. The two returns always move in
exactly opposite directions.
The portfolio risk is very low. It may even be reduced to zero. For example,
if the proportion of investment in P and Q are 0.375 and 0.625 respectively,
portfolio standard deviation becomes:
σp = (0.375)(50) − (0.625)(30) = 0
Here, although the portfolio contains two risky assets, the portfolio has no
risk at all. Thus, the portfolio may become entirely riskfree when security
returns are perfectly negatively correlated. Hence, diversification becomes a
highly productive activity when securities are perfectly negatively correlated,
because portfolio risk can be considerably reduced and sometimes even
eliminated. But, in reality, it is rare to find securities that are perfectly
negatively correlated.
Security Returns Uncorrelated
When the returns of two securities are entirely uncorrelated, the correlation
coefficient would be zero.
The portfolio standard deviation is less than the standard deviations of
individual securities in the portfolio. Thus, when security returns are
uncorrelated, diversification reduces risk and is a productive activity.
We may now tabulate the portfolio standard deviations of our illustrative
portfolio having two securities P and Q, for different values of correlation
coefficients between them. The proportion of investments in P and Q are 0.4
and 0.6 respectively. The individual standard deviations of P and Q are 50
and 30 respectively.
Portfolio Standard Deviations
Correlation
coefficients
Portfolio
standard deviations
1.0
38.00
0.6
34.00
0.0
26.91
−0.6
17.09
−1.0
2.00
From the above analysis we may conclude that diversification reduces risk in
all cases except when the security returns are perfectly positively correlated.
As correlation coefficient declines from +1 to −1, the portfolio standard
deviation also declines. But the risk reduction is greater when the security
returns are negatively correlated.
PORTFOLIOS WITH MORE THAN TWO SECURITIES
So far we have considered a portfolio with only two securities. The benefits
from diversification increase as more and more securities with less than
perfectly positively correlated returns are included in the portfolio. As the
number of securities added to a portfolio increases, the standard deviation of
the portfolio becomes smaller and smaller. Hence, an investor can make the
portfolio risk arbitrarily small by including a large number of securities with
negative or zero correlation in the portfolio.
But, in reality, no securities show negative or even zero correlation.
Typically, securities show some positive correlation, that is above zero but
less than the perfectly positive value (+1). As a result, diversification (that is,
adding securities to a portfolio) results in some reduction in total portfolio
risk but not in complete elimination of risk. Moreover, the effects of
diversification are exhausted fairly rapidly. That is, most of the reduction in
portfolio standard deviation occurs by the time the portfolio size increases to
25 or 30 securities. Adding securities beyond this size brings about only
marginal reduction in portfolio standard deviation.
Adding securities to a portfolio reduces risk because securities are not
perfectly positively correlated. But the effects of diversification are exhausted
rapidly because the securities are still positively correlated to each other
though not perfectly correlated. Had they been negatively correlated, the
portfolio risk would have continued to decline as portfolio size increased.
Thus, in practice, the benefits of diversification are limited.
The total risk of an individual security comprises two components, the
market related risk called systematic risk and the unique risk of that
particular security called unsystematic risk. By combining securities into a
portfolio the unsystematic risk specific to different securities is cancelled out.
Consequently, the risk of the portfolio as a whole is reduced as the size of the
portfolio increases. Ultimately when the size of the portfolio reaches a certain
limit, it will contain only the systematic risk of securities included in the
portfolio. The systematic risk, however, cannot be eliminated. Thus, a fairly
large portfolio has only systematic risk and has relatively little unsystematic
risk. That is why there is no gain in adding securities to a portfolio beyond a
certain portfolio size. Figure 13.1 depicts the diversification of risk in a
portfolio.
The figure shows the portfolio risk declining as the number of securities in
the portfolio increases, but the risk reduction ceases when the unsystematic
risk is eliminated.
RISK-RETURN CALCULATIONS OF PORTFOLIOS WITH
MORE THAN TWO SECURITIES
The expected return of a portfolio is the weighted average of the returns of
individual securities in the portfolio, the weights being the proportion of
investment in each security. The formula for calculation of expected portfolio
return is the same for a portfolio with two securities and for portfolios with
more than two securities. The formula is:
Let us consider a portfolio with four securities having the following
characteristics:
Security
Returns
Proportion of
(per cent)
investment
A
12
0.2
B
17
0.3
C
23
0.1
D
20
0.4
The expected return of this portfolio may be calculated using the formula:
The portfolio variance and standard deviation depend on the proportion of
investment in each security, as also the variance and covariance of each
security included in the portfolio.
The formula for portfolio variance of a portfolio with more than two
securities is as follows:
The method of calculation can be illustrated through an example.
A convenient way to obtain the result is to set up the data required for
calculation in the form of a variance-covariance matrix. Let us consider a
portfolio with three securities A, B and C. The proportion of investment in
each of these securities are 0.20, 0.30 and 0.50 respectively. The variance of
each security and the covariance of each possible pair of securities may be set
up as a matrix as follows:
The entries along the diagonal of the matrix represent the variances of
securities A, B and C. The other entries in the matrix represent the
covariances of the respective pairs of securities such as A and B, A and C, B
and C.
Once the variance-covariance matrix is set up, the computation of portfolio
variance is a comparatively simple operation.
Each cell in the matrix represents a pair of two securities. For example, the
first cell in the first row of the matrix represents A and A; the second cell in
the first row represents securities A and B, and so on. The variance or
covariance in each cell has to be multiplied by the weights of the respective
securities represented by that cell. These weights are available in the matrix
at the left side of the row and the top of the column containing the cell. This
process may be started from the first cell in the first row and continued for all
the cells till the last cell of the last row is reached. When all these products
are summed up, the resulting figure is the portfolio variance. The square root
of this figure gives the portfolio standard deviation.
The variance of the illustrative portfolio given above can now be calculated.
We have seen earlier that covariance between two securities may be
expressed as the product of correlation coefficient between the two securities
and standard deviations of the two securities.
Thus,
σij = rijσiσj
where
σij = Covariance between security i and security j.
rij = Correlation coefficient between security i and security j.
σi = Standard deviation of security i.
σj = Standard deviation of security j.
Hence, the formula for computing portfolio variance may also be stated in the
following form:
To illustrate the use of this formula let us calculate the portfolio variance and
standard deviation for a portfolio with the following characteristics.
Security
xi
σi
Correlation coefficients
P
0.35
7
P and Q = 0.7
Q
0.25
16
P and R = 0.3
R
0.40
9
Q and R = 0.4
It may be noted that correlation coefficient between P and P, Q and Q, R and
R is 1.
The variance-covariance matrix may be set up as follows:
A portfolio is a combination of assets. From a given set of 'n' securities, any
number of portfolios can be created. The portfolios may comprise of two
securities, three securities, all the way up to 'n' securities. A portfolio may
contain the same securities as another portfolio but with different weights.
Thus, new portfolios can be created either by changing the securities in the
portfolio or by changing the proportion of investment in the existing
securities.
Each portfolio is characterised by its expected return and risk. Determining
the expected return and risk (variance or standard deviation) of each portfolio
that can be created from a set of selected securities is the first step in portfolio
management and is called portfolio analysis.
SOLVED EXAMPLES
Example 1 Calculate the expected return and variance of a portfolio
comprising two securities, assuming that the portfolio weights are 0.75 for
security 1 and 0.25 for security 2. The expected return for security 1 is 18 per
cent and its standard deviation is 12 per cent, while the expected return and
standard deviation for security 2 are 22 per cent and 20 per cent respectively.
The correlation between the two securities is 0.6.
Example 2 Consider two securities, P and Q, with expected returns of 15 per
cent and 24 per cent respectively, and standard deviation of 35 per cent and
52 per cent respectively. Calculate the standard deviation of a portfolio
weighted equally between the two securities if their correlation is −0.9.
Example 3 The historical rates of return of two securities over the past ten
years are given. Calculate the covariance and the correlation of the two
securities.
Years
: 1
2
3
4
5
6
7
8
9
10
Security 1 : 12 8
(return
7
14 16 15 18 20 16 22
per cent)
Security 2 : 20 22 24 18 15 20 24 25 22 20
(return
per cent)
For calculation of correlation, the standard deviation of the two securities are
also required.
Calculation of Standard Deviation
Year
R1
R1
2
R2
R2
2
1
12
144
20
400
2
8
64
22
484
3
7
49
24
576
4
14
196
18
324
5
16
256
15
225
6
15
225
20
400
7
18
324
24
576
8
20
400
25
625
9
16
256
22
484
10
22
484
20
400
148
2398
210
4494
Standard deviation of security 1:
Standard devition of security 2:
Example 4 A portfolio is constituted with four securities having the
following characteristics:
Security
Return (per cent)
Proportion of investment
P
17.5
0.15
Q
24.8
0.25
R
15.7
0.45
S
21.3
0.15
Calculate the expected return of the portfolio.
Example 5 Given the following variance-covariance matrix for three
securities, as well as the percentage of the portfolio that each security
comprises, calculate the portfolio’s standard deviation.
Security
A
B
C
A
425
−190
120
B
−190
320
205
C
120
205
175
WA = 0.35
WB = 0.25
WC = 0.40
Solution The formula for the calculation of portfolio variance of a portfolio
with more than two securities is as follows:
Example 6 The estimates of the standard deviations and correlation coefficients for three stocks are given below:
Stock
Standard
Correlation with stock
deviation
A
B
C
A
32
1.00
−0.80
0.40
B
26
−0.80
1.00
0.65
C
18
0.40
0.65
1.00
If a portfolio is constructed with 15 per cent of stock A, 50 per cent of stock B
and 35 per cent of stock C, what is the portfolio’s standard deviation?
Solution Here, the covariances between securities are not given. However,
the covariance between two securities may be expressed as the product of
correlation coefficient between the two securities and standard deviations of
the two securities that is,
σij = rijσiσj
The variance-covariance matrix may therefore be set up as follows:
EXERCISES
1. Use the following data to calculate the variance and standard deviation
for a portfolio containing stocks 1 and 2:
r1,2 = 0.65
σ1 = 13
σ1 = 27
W1 = 0.70
W2 = 0.30
2. Given the following historical data for stocks X and Y, calculate
covariance and correlation coefficient of the two stocks.
Year Annual returns (per cent)
X
Y
1
6.2
− 8.5
2
3.6
− 10.7
3
4.5
12.5
4
2.8
− 5.6
5
1.3
9.4
3. Calculate the expected return of a portfolio with four securities having
the following characteristics:
Security
Return Proportion of
(per cent) investment
W
18.50
0.20
X
23.75
0.10
Y
12.30
0.25
Z
16.85
0.45
4. Calculate the expected return of a portfolio composed of the following
securities:
Security
Expected return
Proportion
(per cent)
(per cent)
1
10
20
2
15
20
3
20
60
What would be the expected return if the proportion of each security in
the portfolio were 25, 25 and 50 per cent respectively?
5. Calculate the portfolio variance and standard deviation for a portfolio
having the following characteristics.
Securities
Return
(per cent)
Standard
deviation
Proportion of
investment
J
40
12
0.2
K
15
8
0.3
L
50
16
0.5
Correlation coefficients:
J and K = 0.8
J and L = 0.2
K and L = 0.5
6. Suppose an analyst has provided you the following estimates in respect
of equity shares of Century, Escorts and ACC:
Security
C
E
A
Expected Monthly returns per cent
5
4
9
Standard deviation per cent
8
7
17
Correlation coefficients of returns between
C and E = 0.4
C and A = 0.6
E and A = 0.3
Assuming that equal amounts of the available funds will be invested in
the three stocks, estimate the portfolio’s mean return and standard
deviation.
7. For the following portfolio, calculate the mean rate of return and
standard deviation:
Security
Proportion
Price
(beginning of year)Rs.
Increase/decrease
during year
Dividend
Rs.
Rs.
Standard
deviation
(per cent)
X
0.35
25
3
1.5
5
Z
0.40
38
5
3.0
10
Y
0.25
63
−4
0
1
Correlation coefficient:
X and Y = 0.01
X and Z = −0.20
Y and Z = 0.70
8. The variance-covariance matrix for three securities is given below:
Security
P
Q
R
P
108
−56
94
Q
−56
214
137
R
94
137
180
Calculate the standard deviation of a portfolio constructed with these
three securities, the proportion of investment in each being
P(0.20) Q(0.50) R(0.30)
REVIEW QUESTIONS
1. Explain the concept and process of portfolio analysis.
2. Illustrate the calculation of the expected return of a portfolio with an
example.
3. Explain the significance of covariance in the estimation of the risk of a
portfolio.
4. Discuss the impact of covariance or correlation between securities in a
portfolio on the portfolio risk.
5. What happens to the risk of a portfolio as more and more securities are
added to the portfolio?
14
PORTFOLIO SELECTION
The objective of every rational investor is to maximise his returns and
minimise the risk. Diversification is the method adopted for reducing risk. It
essentially results in the construction of portfolios. The proper goal of
portfolio construction would be to generate a portfolio that provides the
highest return and the lowest risk. Such a portfolio would be known as the
optimal portfolio. The process of finding the optimal portfolio is described
as portfolio selection.
The conceptual framework and analytical tools for determining the optimal
portfolio in disciplined and objective manner have been provided by Harry
Markowitz in his pioneering work on portfolio analysis described in his 1952
Journal of Finance article1 and subsequent book2 in 1959. His method of
portfolio selection has come to be known as the Markowitz model. In fact,
Markowitz's work marks the beginning of what is known today as modern
portfolio theory.
FEASIBLE SET OF PORTFOLIOS
With a limited number of securities an investor can create a very large
number of portfolios by combining these securities in different proportions.
These constitute the feasible set of portfolios in which the investor can
possibly invest. This is also known as the portfolio opportunity set.
Each portfolio in the opportunity set is characterised by an expected return
and a measure of risk, viz., variance or standard deviation of returns. Not
every portfolio in the portfolio opportunity set is of interest to an investor. In
the opportunity set some portfolios will obviously be dominated by others. A
portfolio will dominate another if it has either a lower standard deviation and
the same expected return as the other, or a higher expected return and the
same standard deviation as the other. Portfolios that are dominated by other
portfolios are known as inefficient portfolios. An investor would not be
interested in all the portfolios in the opportunity set. He would be interested
only in the efficient portfolios.
Efficient Set of Portfolios
To understand the concept of efficient portfolios, let us consider various
combinations of securities and designate them as portfolios 1 to n. The
expected returns of these portfolios may be worked out. The risk of these
portfolios may be estimated by measuring the standard deviation of portfolio
returns. The table below shows illustrative figures for the expected returns
and standard deviations of some portfolios.
Portfolio no.
Expected return
(per cent)
Standard deviation
(Risk)
1
5.6
4.5
2
7.8
5.8
3
9.2
7.6
4
10.5
8.1
5
11.7
8.1
6
12.4
9.3
7
13.5
9.5
8
13.5
11.3
9
15.7
12.7
10
16.8
12.9
If we compare portfolio nos. 4 and 5, for the same standard deviation of 8.1
portfolio no. 5 gives a higher expected return of 11.7, making it more
efficient than portfolio no. 4. Again, if we compare portfolio nos. 7 and 8, for
the same expected return of 13.5 per cent, the standard deviation is lower for
portfolio no. 7, making it more efficient than portfolio no. 8. Thus, the
selection of portfolios by the investor will be guided by two criteria:
1. Given two portfolios with the same expected return, the investor would
prefer the one with the lower risk.
2. Given two portfolios with the same risk, the investor would prefer the
one with the higher expected return.
These criteria are based on the assumption that investors are rational and also
risk-averse. As they are rational they would prefer more return to less return.
As they are risk averse, they would prefer less risk to more risk.
The concept of efficient sets can be illustrated with the help of a graph. The
expected return and standard deviation of portfolios can be depicted on an XY
graph, measuring the expected return on the Y axis and the standard deviation
on the X axis. Figure 14.1 depicts such a graph.
As each possible portfolio in the opportunity set or feasible set of portfolios
has an expected return and standard deviation associated with it, each
portfolio would be represented by a single point in the risk-return space
enclosed within the two axes of the graph. The shaded area in the graph
represents the set of all possible portfolios that can be constructed from a
given set of securities. This opportunity set of portfolios takes a concave
shape because it consists of portfolios containing securities that are less than
perfectly correlated with each other.
Let us closely examine the diagram in Fig. 14.1. Consider portfolios F and E.
Both the portfolios have the same expected return but portfolio E has less
risk. Hence, portfolio E would be preferred to portfolio F. Now consider
portfolios C and E. Both have the same risk, but portfolio E offers more
return for the same risk. Hence, portfolio E would be preferred to portfolio C.
Thus, for any point in the risk-return space, an investor would like to move as
far as possible in the direction of increasing returns and also as far as possible
in the direction of decreasing risk. Effectively, he would be moving towards
the left in search of decreasing risk and upwards in search of increasing
returns.
Let us consider portfolios C and A. Portfolio C would be preferred to
portfolio A because it offers less risk for the same level of return. In the
opportunity set of portfolios represented in the diagram, portfolio C has the
lowest risk compared to all other portfolios. Here portfolio C in this diagram
represents the global minimum variance portfolio.
Comparing portfolios A and B, we find that portfolio B is preferable to
portfolio A because it offers higher return for the same level of risk. In this
diagram, point B represents the portfolio with the highest expected return
among all the portfolios in the feasible set.
Thus, we find that portfolios lying in the north west boundary of the shaded
area are more efficient than all the portfolios in the interior of the shaded
area. This boundary of the shaded area is called the Efficient Frontier
because it contains all the efficient portfolios in the opportunity set. The set
of portfolios lying between the global minimum variance portfolio and the
maximum return portfolio on the efficient frontier represents the efficient set
of portfolios. The efficient frontier is shown separately in Fig. 14.2.
The efficient frontier is a concave curve in the risk-return space that extends
from the minimum variance portfolio to the maximum return portfolio.
SELECTION OF OPTIMAL PORTFOLIO
The portfolio selection problem is really the process of delineating the
efficient portfolios and then selecting the best portfolio from the set.
Rational investors will obviously prefer to invest in the efficient portfolios.
The particular portfolio that an individual investor will select from the
efficient frontier will depend on that investor's degree of aversion to risk. A
highly risk averse investor will hold a portfolio on the lower left hand
segment of the efficient frontier, while an investor who is not too risk averse
will hold one on the upper portion of the efficient frontier.
The selection of the optimal portfolio thus depends on the investor's risk
aversion, or conversely on his risk tolerance. This can be graphically
represented through a series of risk return utility curves or indifference
curves. The indifference curves of an investor are shown in Fig. 14.3. Each
curve represents different combinations of risk and return all of which are
equally satisfactory to the concerned investor. The investor is indifferent
between the successive points in the curve. Each successive curve moving
upwards to the left represents a higher level of satisfaction or utility. The
investor's goal would be to maximise his utility by moving upto the higher
utility curve. The optimal portfolio for an investor would be the one at the
point of tangency between the efficient frontier and his risk-return utility or
indifference curve.
This is shown in Fig. 14.3. The point O′ represents the optimal portfolio.
Markowitz used the technique of quadratic programming to identify the
efficient portfolios. Using the expected return and risk of each security under
consideration and the covariance estimates for each pair of securities, he
calculated risk and return for all possible portfolios. Then, for any specific
value of expected portfolio return, he determined the least risk portfolio using
quadratic programming. With another value of expected portfolio return, a
similar procedure again gives the minimum risk portfolio. The process is
repeated with different values of expected return, the resulting minimum risk
portfolios constitute the set of efficient portfolios.
LIMITATIONS OF MARKOWITZ MODEL
One of the main problems with the Markowitz model is the large number of
input data required for calculations. An investor must obtain estimates of
return and variance of returns for all securities as also covariances of returns
for each pair of securities included in the portfolio. If there are N securities in
the portfolio, he would need N return estimates, N variance estimates and
N(N − 1)/2 covariance estimates, resulting in a total of 2N + [N(N − 1)/2]
estimates. For example, analysing a set of 200 securities would require 200
return estimates, 200 variance estimates and 19,900 covariance estimates,
adding upto a total of 20,300 estimates. For a set of 500 securities, the
estimates required would be 1,25,750. It may be noted that the number of
estimates required becomes large because covariances between each pair of
securities have to be estimated.
The second difficulty with the Markowitz model is the complexity of
computations required. The computations required are numerous and
complex in nature. With a given set of securities infinite number of portfolios
can be constructed. The expected returns and variances of returns for each
possible portfolio have to be computed. The identification of efficient
portfolios requires the use of quadratic programming which is a complex
procedure.
Because of the difficulties associated with the Markowitz model, it has found
little use in practical applications of portfolio analysis. Much simplification is
needed before the theory can be used for practical applications.
Simplification is needed in the amount and type of input data required to
perform portfolio analysis; simplification is also needed in the computational
procedure used to select optimal portfolios.
The simplification is achieved through index models. There are essentially
two types of index models: single index model and multi-index model. The
single index model is the simplest and the most widely used simplification
and may be regarded as being at one extreme point of a continuum, with the
Markowitz model at the other extreme point. Multi-index models may be
placed at the mid region of this continuum of portfolio analysis techniques.
SINGLE INDEX MODEL
The basic notion underlying the single index model is that all stocks are
affected by movements in the stock market. Casual observation of share
prices reveals that when the market moves up (as measured by any of the
widely used stock market indices), prices of most shares tend to increase.
When the market goes down, the prices of most shares tend to decline. This
suggests that one reason why security returns might be correlated and there is
co-movement between securities, is because of a common response to market
changes. This co-movement of stocks with a market index may be studied
with the help of a simple linear regression analysis, taking the returns on an
individual security as the dependent variable (Ri) and the returns on the
market index (Rm) as the independent variable.
The return of an individual security is assumed to depend on the return on the
market index. The return of an individual security may be expressed as:
Ri = αi + βi Rm + ei
where
αi = Component of security i’s return that is independent of the market's
performance.
Rm = Rate of return on the market index.
βi = Constant that measures the expected change in Ri given a change in
Rm.
ei = Error term representing the random or residual return.
This equation breaks the return on a stock into two components, one part due
to the market and the other part independent of the market. The beta
parameter in the equation, βi, measures how sensitive a stock’s return is to the
return on the market index. It indicates how extensively the return of a
security will vary with changes in the market return. For example, if the βi of
a security is 2, then the return of the security is expected to increase by 20 per
cent when the market return increases by 10 per cent. In this case, if the
market return decreases by 10 per cent, the security return is expected to
decrease by 20 per cent. For a security with βi of 0.5, when the market return
increases or decreases by 10 per cent, the security return is expected to
increase or decrease by 5 per cent (that is 10 × 0.5). A beta coefficient greater
than one would suggest greater responsiveness on the part of the stock in
relation to the market and vice versa.
The alpha parameter αi indicates what the return of the security would be
when the market return is zero. For example, a security with an alpha of +3
per cent would earn 3 per cent return even when the market return is zero and
it would earn an additional 3 per cent at all levels of market return.
Conversely, a security with an alpha of −4.5 per cent would lose 4.5 per cent
when the market return is zero, and would earn 4.5 per cent less at all levels
of market return. The positive alpha thus represents a sort of bonus return and
would be a highly desirable aspect of a security, whereas a negative alpha
represents a penalty to the investor and is an undesirable aspect of a security.
The final term in the equation, ei, is the unexpected return resulting from
influences not identified by the model. It is referred to as the random or
residual return. It may take on any value, but over a large number of
observations it will average out to zero.
William Sharpe, who tried to simplify the data inputs and data tabulation
required for the Markowitz model of portfolio analysis, suggested that a
satisfactory simplification would be achieved by abandoning the covariance
of each security with each other security and substituting in its place the
relationship of each security with a market index as measured by the single
index model suggested above. This is known as Sharpe index model.
In the place of [N(N − 1)/2] covariances required for the Markowitz model,
Sharpe model would requires only N measures of beta coefficients.
Measuring Security Return and Risk under Single Index Model
Using the single index model, expected return of an individual security may
be expressed as:
The market related component of risk is referred to as systematic risk as it
affects all securities. The specific risk component is the unique risk or
unsystematic risk which can be reduced through diversification. It is also
called diversifiable risk.
Measuring Portfolio Return and Risk under Single Index
Model
Portfolio analysis and selection require as inputs the expected portfolio return
and risk for all possible portfolios that can be constructed with a given set of
securities. The return and risk of portfolios can be calculated using the single
index model.
The expected return of a portfolio may be taken as portfolio alpha plus
portfolio beta times expected market return. Thus,
The expected return of the portfolio is the sum of the weighted average of the
specific returns and the weighted average of the market related returns of
individual securities.
The risk of a portfolio is measured as the variance of the portfolio returns.
The risk of a portfolio is simply a weighted average of the market related
risks of individual securities plus a weighted average of the specific risks of
individual securities in the portfolio. The portfolio risk may be expressed as:
The first term constitutes the variance of the market index multiplied by the
square of portfolio beta and represents the market related risk (or systematic
risk) of the portfolio. The second term is the weighted average of the
variances of residual returns of individual securities and represents the
specific risk or unsystematic risk of the portfolio.
As more and more securities are added to the portfolio, the unsystematic risk
of the portfolio becomes smaller and is negligible for a moderately sized
portfolio. Thus, for a large portfolio, the residual risk or unsystematic risk
approaches zero and the portfolio risk becomes equal to . Hence, the effective
measure of portfolio risk is βp.
Let us consider a hypothetical portfolio of four securities. The table below
shows the basic input data such as weightage, alphas, betas and residual
variances of the individual securities required for calculating portfolio return
and variance.
Using the expected portfolio returns and portfolio variances calculated with
the single index model, the set of efficient portfolios is generated by means of
the same quadratic programming routine as used in the Markowitz model.
MULTI-INDEX MODEL
The single index model is in fact an oversimplification. It assumes that stocks
move together only because of a common co-movement with the market.
Many researchers have found that there are influences other than the market
that cause stocks to move together. Multi-index models attempt to identify
and incorporate these non-market or extra-market factors that cause securities
to move together also into the model. These extra-market factors are a set of
economic factors that account for common movement in stock prices beyond
that accounted for by the market index itself. Fundamental economic
variables such as inflation, real economic growth, interest rates, exchange
rates etc. would have a significant impact in determining security returns and
hence, their co-movement.
A multi-index model augments the single index model by incorporating these
extra market factors as additional independent variables. For example, a
multi-index model incorporating the market effect and three extra-market
effects takes the following form:
Ri = αi + βmRm + β1R1 + β2R2 + β3R3 + ei
The model says that the return of an individual security is a function of four
factors—the general market factor Rm and three extra-market factors R1, R2
and R3. The beta coefficients attached to the four factors have the same
meaning as in the single index model. They measure the sensitivity of the
stock return to these factors. The alpha parameter αi and the residual term ei
also have the same meaning as in the single index model.
Calculation of return and risk of individual securities as well as portfolio
return and variance follows the same pattern as in the single index model.
These values can then be used as inputs for portfolio analysis and selection.
A multi-index model is an alternative to the single index model. However, it
is more complex and requires more data estimates for its application. Both
the single index model and the multi-index model have helped to make
portfolio analysis more practical.
SOLVED EXAMPLES
Example 1 An investor owns a portfolio whose market model is estimated as:
Rp = 2.3 + 0.85 Rm + ep
If the expected return on the market index is 17.5 per cent, what is the
expected return on the investor’s portfolio?
Solution Assuming that ep = 0
Rp = 2.3 + 0.85 (17.5)
= 2.3 + 14.875
= 17.175 per cent
Example 2 An investor owns a portfolio composed of five securities with the
following characteristics:
Security
Beta
Random error term
Proportion
standard deviation (per cent)
1
1.35
5
0.10
2
1.05
9
0.20
3
0.80
4
0.15
4
1.50
12
0.30
5
1.12
8
0.25
Example 3 Consider a portfolio composed of five securities. All the
securities have a beta of 1.0 and unique or specific risk (standard deviation)
of 25 per cent. The portfolio distributes weight equally among its component
securities. If the standard deviation of the market index is 18 per cent,
calculate the total risk of the portfolio.
Solution The input data may be arranged in the form of the following table:
Security
Beta
Specific risk
Proportion
(Standard deviation)
1
1.0
25
0.2
2
1.0
25
0.2
3
1.0
25
0.2
4
1.0
25
0.2
5
1.0
25
0.2
Example 4 How many parameters must be estimated to analyse the riskreturn profile of a 50-stock portfolio using (a) the original Markowitz model,
and (b) the Sharpe single index model?
Example 5 Consider a portfolio of four securities with the following
characteristics:
Security
Weighting
αi
βi
Residual variance ()
1
0.2
2.0
1.2
320
2
0.3
1.7
0.8
450
3
0.1
−0.8
1.6
270
4
0.4
1.2
1.3
180
Calculate the return and risk of the portfolio under single index model, if the
return on market index is 16.4 per cent and the standard deviation of return
on market index is 14 per cent.
Example 6 The data for three stocks are given. The data are obtained from
correlating returns on these stocks with the returns on the market index.
Stock
αi
βi
Residual variance (per cent) (σ ei)
1
−2.1
1.6
14
2
1.8
0.4
8
3
1.2
1.3
18
2
Which single stock would an investor prefer to own from a risk-return view
point if the market index were expected to have a return of 15 per cent and a
variance of return of 20 per cent?
Solution Here we have to calculate the expected return and risk of each
security under the single index model.
EXERCISES
1. Consider a portfolio of six securities with the following characteristics:
Security
Weighting
αi
βi
1
0.10
−0.28
0.91
23
2
0.15
0.76
0.87
60
3
0.20
2.52
1.17
52
4
0.10
−0.16
0.97
86
5
0.25
1.55
1.07
67
6
0.20
0.47
0.86
82
2
Residual variance (per cent) σ
ei
Assuming the return on market index to be 14.5 per cent and the
standard deviation of return on market index to be 16 per cent, calculate
the portfolio return and risk under single index model.
2. The data for four stocks are given. The data are the result of correlating
returns on these stocks with the returns on the market index.
Stock
αi
βi
A
−1.50
1.25
24
B
2.15
1.47
47
C
1.70
0.69
36
D
0.83
0.88
30
2
Residual variance (per cent) σ
ei
The market index is expected to have a return of 17.5 per cent and a
variance of return of 28 per cent.
Which single stock would an investor prefer to own from a risk- return
perspective?
3. An investor owns a portfolio of four securities with the following
characteristics:
Security
Beta
Random error
Proportion
(Standard deviation) (per cent)
1
0.79
12
0.25
2
1.85
8
0.30
3
1.05
17
0.15
4
0.82
20
0.30
Calculate the portfolio risk, assuming the standard deviation of returns
on market index to be 16 per cent.
REVIEW QUESTIONS
1. Explain the concept of efficient frontier in the context of portfolio
selection.
2. Distinguish between the feasible set of portfolios and the efficient set of
portfolios.
3. What is meant by optimal portfolio? How is it identified?
4. Explain the problem involved in the portfolio selection process.
5. List the limitations of Markowitz model of portfolio selection.
6. Describe the Sharpe single index model. How do you interpret α and β
parameters in the model?
7. Illustrate, with suitable examples, how security return and risk are
estimated under single index model.
8. “The single index model results in a substantial reduction in inputs
required for portfolio analysis.” Elucidate.
9. Explain how portfolio return and risk are estimated under single index
model.
10. Write a note on multi-index models for portfolio analysis.
REFERENCES
1. Markowitz, Harry, 1952, “Portfolio Selection”, Journal of Finance, pp.
77−91.
2. Markowitz, Harry, 1959, Portfolio Selection: Efficient Diversification of
Investments, John Wiley & Sons, New York.
15
CAPITAL ASSET PRICING
MODEL (CAPM)
The capital asset pricing model was developed in mid-1960s by three
researchers William Sharpe, John Lintner and Jan Mossin independently.
Consequently, the model is often referred to as Sharpe-Lintner-Mossin
Capital Asset Pricing Model.
The capital asset pricing model or CAPM is really an extension of the
portfolio theory of Markowitz. The portfolio theory is a description of how
rational investors should build efficient portfolios and select the optimal
portfolio. The capital asset pricing model derives the relationship between the
expected return and risk of individual securities and portfolios in the capital
markets if everyone behaved in the way the portfolio theory suggested.
Let us, therefore, begin by summarising the fundamental notions of portfolio
theory.
FUNDAMENTAL NOTIONS OF PORTFOLIO THEORY
Return and risk are two important characteristics of every investment.
Investors base their investment decision on the expected return and risk of
investments. Risk is measured by the variability in returns.
Investors attempt to reduce the variability of returns through diversification
of investment. This results in the creation of a portfolio. With a given set of
securities, any number of portfolios may be created by altering the proportion
of funds invested in each security. Among these portfolios some dominate
others, or some are more efficient than the vast majority of portfolios because
of lower risk or higher returns. Investors identify this efficient set of
portfolios.
Diversification helps to reduce risk, but even a well diversified portfolio does
not become risk free. If we construct a portfolio including all the securities in
the stock market, that would be the most diversified portfolio. Even such a
portfolio would be subject to considerable variability. This variability is
undiversifiable and is known as the market risk or systematic risk because
it affects all the securities in the market.
The real risk of a security is the market risk which cannot be eliminated
through diversification. This is indicated by the sensitivity of a security to the
movements of the market and is measured by the beta coefficient of the
security.
A rational investor would expect the return on a security to be commensurate
with its risk. The higher the risk of a security, the higher would be the return
expected from it. And since the relevant risk of a security is its market risk or
systematic risk, the return is expected to be correlated with this risk only. The
capital asset pricing model gives the nature of the relationship between the
expected return and the systematic risk of a security.
ASSUMPTIONS OF CAPM
The capital asset pricing model is based on certain explicit assumptions
regarding the behaviour of investors. The assumptions are listed below:
1. Investors make their investment decisions on the basis of risk-return
assessments measured in terms of expected returns and standard
deviation of returns.
2. The purchase or sale of a security can be undertaken in infinitely
divisible units.
3. Purchases and sales by a single investor cannot affect prices. This means
that there is perfect competition where investors in total determine prices
by their actions.
4. There are no transaction costs. Given the fact that transaction costs are
small, they are probably of minor importance in investment decisionmaking, and hence they are ignored.
5. There are no personal income taxes. Alternatively, the tax rates on
dividend income and capital gains are the same, thereby making the
investor indifferent o the form in which the return on the investment is
received (dividends or capital gains).
6. The investor can lend or borrow any amount of funds desired at a rate of
interest equal to the rate for riskless securities.
7. The investor can sell short any amount of any shares.
8. Investors share homogeneity of expectations. This implies that investors
have identical expectations with regard to the decision period and
decision inputs. Investors are presumed to have identical holding periods
and also identical expectations regarding expected returns, variances of
expected returns and covariances of all pairs of securities.
It is true that many of the above assumptions are untenable. However, they do
not materially alter the real world. Moreover, the model describes the risk
return relationship and the pricing of assets fairly well.
EFFICIENT FRONTIER WITH RISKLESS LENDING AND
BORROWING
The portfolio theory deals with portfolios of risky assets. According to the
theory, an investor faces an efficient frontier containing the set of efficient
portfolios of risky assets. Now it is assumed that there exists a riskless asset
available for investment. A riskless asset is one whose return is certain such
as a government security. Since the return is certain, the variability of return
or risk is zero. The investor can invest a portion of his funds in the riskless
asset which would be equivalent to lending at the risk free asset’s rate of
return, namely Rf. He would then be investing in a combination of risk free
asset and risky assets.
Similarly, it may be assumed that an investor may borrow at the same risk
free rate for the purpose of investing in a portfolio of risky assets. He would
then be using his own funds as well as some borrowed funds for investment.
The efficient frontier arising from a feasible set of portfolios of risky assets is
concave in shape. When an investor is assumed to use riskless lending and
borrowing in his investment activity the shape of the efficient frontier
transforms into a straight line. Let us see how this happens.
Consider Fig. 15.1. The concave curve ABC represents an efficient frontier of
risky portfolios. B is the optimal portfolio in the efficient frontier with Rp =
15 per cent and σp = 8 per cent. A risk free asset with rate of return Rf = 7 per
cent is available for investment. The risk or standard deviation of this asset
would be zero because it is a riskless asset. Hence, it would be plotted on the
Y axis. The investor may lend a part of his money at the riskless rate, i.e.
invest in the risk free asset and invest the remaining portion of his funds in a
risky portfolio.
If an investor places 40 per cent of his funds in the riskfree asset and the
remaining 60 per cent in portfolio B, the return and risk of this combined
portfolio O′ may be calculated using the following formulas.
Return
Rc =ωRm + (1 − ω)Rf
where
Rc = Expected return on the combined portfolio.
ω = Proportion of funds invested in risky portfolio.
(1 −ω) = Proportion of funds invested in riskless asset.
Rm = Expected return on risky portfolio.
Rf = Rate of return on riskless asset.
Risk
σc = ωσm + (1 − ω)σf
where
σc = Standard deviation of the combined portfolio.
ω = Proportion of funds invested in risky portfolio.
σm = Standard deviation of risky portfolio.
σf = Standard deviation of riskless asset.
The second term on the right hand side of the equation, (1 − ω)σf would be
zero as σf = zero. Hence, the formula may be reduced as
σc = ωσm
The return and risk of the combined portfolio in our illustration is worked out
below:
Rc = (0.60)(15) + (0.40)(7)
= 11.8 per cent
σc = (0.60) (8) = 4.8 per cent
Both return and risk are lower than those of the risky portfolio B.
If we change the proportion of investment in the risky portfolio to 75 per
cent, the return and risk of the combined portfolio may be calculated as
shown below:
Rc = (0.75)(15) + (0.25)(7)
= 13 per cent
σc = (0.75)(8) = 6 per cent
Here again, both return and risk are lower than those of the risky portfolio B.
Similarly, the return and risk of all possible combinations of the riskless asset
and the risky portfolio B may be worked out. All these points will lie in the
straight line from Rf to B in Fig. 15.1.
Now, let us consider borrowing funds by the investor for investing in the
risky portfolio an amount which is larger than his own funds.
If ω is the proportion of investor's funds invested in the risky portfolio, then
we can envisage three situations. If ω = 1, the investor's funds are fully
committed to the risky portfolio. If ω < 1, only a fraction of the funds is
invested in the risky portfolio and the remainder is lend at the risk free rate. If
ω > 1, it means the investor is borrowing at the risk free rate and investing an
amount larger than his own funds in the risky portfolio.
The return and risk of such a levered portfolio can be calculated as follows:
RL = ωRm − (ω − 1)Rf
where
RL = Return on the levered portfolio.
ω = Proportion of investor's funds invested in the risky portfolio.
Rm = Return on the risky portfolio.
Rf = The risk free borrowing rate which would be the same as the risk free
lending rate, namely the return on the riskless asset.
The first term of the equation represents the gross return earned by investing
the borrowed funds as well as investor's own funds in the risky portfolio. The
second term of the equation represents the cost of borrowing funds which is
deducted from the gross returns to obtain the net return on the levered
portfolio.
The risk of the levered portfolio can be calculated as:
σL = ωσm
The return and risk of the investor in our illustration may be calculated
assuming ω = 1.25
RL = (1.25)(15) − (0.25)(7)
= 17 per cent
σL = (1.25)(8)
= 10 per cent
The return and risk of the levered portfolio are larger than those of the risky
portfolio. The levered portfolio would give increased returns with increased
risk. The return and risk of all levered portfolios would lie in a straight line to
the right of the risky portfolio B. This is depicted in Fig. 15.2.
Thus, the introduction of borrowing and lending gives us an efficient frontier
that is a straight line throughout. This line sets out all the alternative
combinations of the risky portfolio B with risk free borrowing and lending.
The line segment from Rf to B includes all the combinations of the risky
portfolio and the risk free asset. The line segment beyond point B represents
all the levered portfolios (that is combinations of the risky portfolio with
borrowing). Borrowing increases both the expected return and the risk, while
lending (that is, combining the risky portfolio with risk free asset) reduces the
expected return and risk. Thus, the investor can use borrowing or lending to
attain the desired risk level. Those investors with a high risk aversion will
prefer to lend and thus, hold a combination of risky assets and the risk free
asset. Others with less risk aversion will borrow and invest more in the risky
portfolio.
THE CAPITAL MARKET LINE
All investors are assumed to have identical (homogeneous) expectations.
Hence, all of them will face the same efficient frontier depicted in Fig. 15.2.
Every investor will seek to combine the same risky portfolio B with different
levels of lending or borrowing according to his desired level of risk. Because
all investors hold the same risky portfolio, then it will include all risky
securities in the market. This portfolio of all risky securities is referred to as
the market portfolio M. Each security will be held in the proportion which the
market value of the security bears to the total market value of all risky
securities in the market. All investors will hold combinations of only two
assets, the market portfolio and a riskless security.
All these combinations will lie along the straight line representing the
efficient frontier. This line formed by the action of all investors mixing the
market portfolio with the risk free asset is known as the capital market line
(CML). All efficient portfolios of all investors will lie along this capital
market line.
The relationship between the return and risk of any efficient portfolio on the
capital
market line can be expressed in the form of the following equation.
where the subscript e denotes an efficient portfolio.
The risk free return Rf represents the reward for waiting. It is, in other words,
the price of time. The term represents the price of risk or risk premium, i.e.
the excess return earned per unit of risk or standard deviation. It measures the
additional return for an additional unit of risk. When the risk of the efficient
portfolio, σe, is multiplied with this term, we get the risk premium available
for the particular efficient portfolio under consideration.
Thus, the expected return on an efficient portfolio is:
(Expected return) = (Price of time) + (Price of risk) (Amount of risk)
The CML provides a risk return relationship and a measure of risk for
efficient portfolios. The appropriate measure of risk for an efficient portfolio
is the standard deviation of return of the portfolio. There is a linear
relationship between the risk as measured by the standard deviation and the
expected return for these efficient portfolios.
THE SECURITY MARKET LINE
The CML shows the risk-return relationship for all efficient portfolios. They
would all lie along the capital market line. All portfolios other than the
efficient ones will lie below the capital market line. The CML does not
describe the risk-return relationship of inefficient portfolios or of individual
securities. The capital asset pricing model specifies the relationship between
expected return and risk for all securities and all portfolios, whether efficient
or inefficient.
We have seen earlier that the total risk of a security as measured by standard
deviation is composed of two components: systematic risk and unsystematic
risk or diversifiable risk. As investment is diversified and more and more
securities are added to a portfolio, the unsystematic risk is reduced. For a
very well diversified portfolio, unsystematic risk tends to become zero and
the only relevant risk is systematic risk measured by beta (β). Hence, it is
argued that the correct measure of a security’s risk is beta.
It follows that the expected return of a security or of a portfolio should be
related to the risk of that security or portfolio as measured by β. Beta is a
measure of the security's sensitivity to changes in market return. Beta value
greater than one indicates higher sensitivity to market changes, whereas beta
value less than one indicates lower sensitivity to market changes. A β value
of one indicates that the security moves at the same rate and in the same
direction as the market. Thus, the β of the market may be taken as one.
The relationship between expected return and β of a security can be
determined graphically. Let us consider an XY graph where expected returns
are plotted on the Y axis and beta coefficients are plotted on the X axis. A risk
free asset has an expected return equivalent to Rf and beta coefficient of zero.
The market portfolio M has a beta coefficient of one and expected return
equivalent to . A straight line joining these two points is known as the
security market line (SML). This is illustrated in Fig. 15.3.
The security market line provides the relationship between the expected
return and beta of a security or portfolio. This relationship can be expressed
in the form of the following equation:
A part of the return on any security or portfolio is a reward for bearing risk
and the rest is the reward for waiting, representing the time value of money.
The risk free rate, Rf (which is earned by a security which has no risk) is the
reward for waiting. The reward for bearing risk is the risk premium. The risk
premium of a security is directly proportional to the risk as measured by β.
The risk premium of a security is calculated as the product of beta and the
risk premium of the market which is the excess of expected market return
over the risk free return, that is,
. Thus,
Expected return on a security = Risk free return + (Beta × Risk premium of
market)
CAPM
The relationship between risk and return established by the security market
line is known as the capital asset pricing model. It is basically a simple
linear relationship. The higher the value of beta, higher would be the risk of
the security and therefore, larger would be the return expected by the
investors. In other words, all securities are expected to yield returns
commensurate with their riskiness as measured by β. This relationship is
valid not only for individual securities, but is also valid for all portfolios
whether efficient or inefficient.
The expected return on any security or portfolio can be determined from the
CAPM formula if we know the beta of that security or portfolio. To illustrate
the application of the CAPM, let us consider a simple example. There are two
securities P and Q having values of beta as 0.7 and 1.6 respectively. The risk
free rate is assumed to be 6 per cent and the market return is expected to be
15 per cent, thus providing a market risk premium of 9 per cent (i.e.
− Rf).
Security P with a β of 0.7 has an expected return of 12.3 per cent whereas
security Q with a higher beta of 1.6 has a higher expected return of 20.4 per
cent.
CAPM represents one of the most important discoveries in the field of
finance. It describes the expected return for all assets and portfolios of assets
in the economy. The difference in the expected returns of any two assets can
be related to the difference in their betas. The model postulates that
systematic risk is the only important ingredient in determining expected
return. As investors can eliminate all unsystematic risk through
diversification, they can be expected to be rewarded only for bearing
systematic risk. Thus, the relevant risk of an asset is its systematic risk and
not the total risk.
SML AND CML
It is necessary to contrast SML with CML. Both postulate a linear (straight
line) relationship between risk and return. In CML the risk is defined as total
risk and is measured by standard deviation, while in SML the risk is defined
as systematic risk and is measured by β. Capital market line is valid only for
efficient portfolios while security market line is valid for all portfolios and all
individual securities as well. CML is the basis of the capital market theory
while SML is the basis of the capital asset pricing model.
PRICING OF SECURITIES WITH CAPM
The capital asset pricing model can also be used for evaluating the pricing of
securities. The CAPM provides a framework for assessing whether a security
is underpriced, overpriced or correctly priced. According to CAPM, each
security is expected to provide a return commensurate with its level of risk. A
security may be offering more returns than the expected return, making it
more attractive. On the contrary, another security may be offering less return
than the expected return, making it less attractive.
The expected return on a security can be calculated using the CAPM formula.
Let us designate it as the theoretical return. The real rate of return estimated
to be realised from investing in a security can be calculated by the following
formula:
This may be designated as the estimated return.
The CAPM framework for evaluation of pricing of securities can be
illustrated with Fig. 15.4.
Figure 15.4 shows the security market line. Beta values are plotted on the X
axis, while estimated returns are plotted on the Y axis. Nine securities are
plotted on the graph according to their beta values and estimated return
values.
Securities A, L and P are in the same risk class having an identical beta value
of 0.7. The security market line shows the expected return for each level of
risk. Security L plots on the SML indicating that the estimated return and
expected return on security L is identical. Security A plots above the SML
indicating that its estimated return is higher than its theoretical return. It is
offering higher return than what is commensurate with its risk. Hence, it is
attractive and is presumed to be underpriced. Stock P which plots below the
SML has an estimated return which is lower than its theoretical or expected
return. This makes it undesirable. The security may be considered to be
overpriced.
Securities B, M and Q constitute a set of securities in the same risk class.
Security B may be assumed to be underpriced because it offers more return
than expected, while security Q may be assumed to be overpriced as it offers
lower return than that expected on the basis of its risk. Security M can be
considered to be correctly priced as it provides a return commensurate with
its risk.
Securities C, N and R constitute another set of securities belonging to the
same risk class, each having a beta value of 1.3. It can be seen that security C
is underpriced, security R is overpriced and security N is correctly priced.
Thus, in the context of the security market line, securities that plot above the
line presumably are underpriced because they offer a higher return than that
expected from securities with the same risk. On the other hand, a security is
presumably overpriced if it plots below the SML because it is estimated to
provide a lower return than that expected from securities in the same risk
class. Securities which plot on SML are assumed to be appropriately priced in
the context of CAPM. These securities are offering returns in line with their
riskiness.
Securities plotting off the security market line would be evidence of
mispricing in the market place. CAPM can be used to identify underpriced
and overpriced securities. If the expected return on a security calculated
according to CAPM is lower than the actual or estimated return offered by
that security, the security will be considered to be underpriced. On the
contrary, a security will be considered to be overpriced when the expected
return on the security according to CAPM formulation is higher than the
actual return offered by the security.
Let us consider an example. The estimated rates of return and beta
coefficients of some securities are as given below:
Security Estimated returns Beta
(per cent)
A
30
1.6
B
24
1.4
C
18
1.2
D
15
0.9
E
15
1.1
F
12
0.7
The risk free rate of return is 10 per cent; while the market return is expected
to be 18 per cent.
Similarly, the expected return on each security can be calculated by
substituting the beta value of each security in the equation.
The expected return according to CAPM formula and the estimated return of
each security are tabulated below:
Security
Expected return
(CAPM)
Estimated
return
A
22.8
30
B
21.2
24
C
19.6
18
D
17.2
15
E
18.8
15
F
15.6
12
Securities A and B provide more return than the expected return and hence
may be assumed to be underpriced. Securities C, D, E and F may be assumed
to be overpriced as each of them provides lower return compared to the
expected return.
In this chapter we have seen two equations representing risk return
relationships. The first of these was the capital market line which describes
the risk return relationship for efficient portfolios. The second was the
security market line describing the risk return relationship for all portfolios as
well as individual securities. This formula is also known as the capital asset
pricing model or CAPM. It postulates that every security is expected to earn
a return commensurate with its risk as measured by beta. CAPM establishes a
linear relationship between the expected return and systematic risk of all
assets. This relation can be used to evaluate the pricing of assets.
SOLVED EXAMPLES
Example 1 Security J has a beta of 0.75 while security K has a beta of 1.45.
Calculate the expected return for these securities, assuming that the risk free
rate is 5 per cent and the expected return of the market is 14 per cent.
Example 2 A security pays a dividend of ` 3.85 and sells currently at ` 83.
The security is expected to sell at ` 90 at the end of the year. The security has
a beta of 1.15. The risk free rate is 5 per cent and the expected return on
market index is 12 per cent. Assess whether the security is correctly priced.
Solution To assess whether a security is correctly priced, we need to
calculate (a) the expected return as per CAPM formula, (b) the estimated
return on the security based on the dividend and increase in price over the
holding period.
As the estimated return on the security is more or less equal to the expected
return, the security can be assessed as fairly priced.
Example 3 The following data are available to you as portfolio manager:
Security
Estimated
return (per cent)
Beta
Standard deviation
(per cent)
A
30
2.0
50
B
25
1.5
40
C
20
1.0
30
D
11.5
0.8
25
E
10.0
0.5
20
Market index
15
1.0
18
Govt. security
7
0
0
(a) In terms of the security market line, which of the securities listed above
are underpriced?
(b) Assuming that a portfolio is constructed using equal proportions of the
five securities listed above, calculate the expected return and risk of such
a portfolio.
The equation becomes
The expected return as per CAPM formula and the estimated return of each
security can be tabulated.
Security
Expected
return (per cent)
Estimated
return (per cent)
A
23.0
30.0
B
19.0
25.0
C
15.0
20.0
D
13.4
11.5
E
11.0
10.0
A security whose estimated return is greater than the expected return is
assumed to be underpriced because it offers a higher return than that expected
from securities with the same risk.
Accordingly, securities A, B and C are underpriced.
EXERCISES
1. A security currently sells for ` 125. It is expected to pay a dividend of `
4.25 and be sold for ` 140 at the end of the year. The security has a beta
of 1.42. The risk free rate in the market is 6 per cent and the expected
return on a representative market index is 15 per cent. Assess whether
the security is correctly priced.
2. The estimated rates of return, beta coefficients and standard deviations
of some securities are as given below:
Security
Estimated
Beta Standard deviation
return (per cent)
(per cent)
A
35
1.60
50
B
28
1.40
40
C
21
1.10
30
D
18
0.90
25
E
15
0.75
20
F
12
0.60
18
The risk free rate of return is 8 per cent. The market return is expected to
be 20 per cent.
Determine which of the above securities are overpriced and which are
underpriced?
3. The following data are available to you as a portfolio manager:
Security
Estimated
Beta Standard deviation
return (per cent)
(per cent)
1
32
2.10
50
2
30
1.80
35
3
25
1.65
42
4
20
1.30
26
5
18
1.15
29
6
15
0.85
18
7
14
0.75
20
8
12
0.50
17
Market index
16
1.00
25
Govt. security
7.5
0
0
(a) In terms of security market line, which of the securities listed above
are undervalued?
(b) Assuming that a portfolio is constructed investing equal proportion
of funds in each of the above securities, what is the expected return
and risk of such a portfolio.
REVIEW QUESTIONS
1. List the assumptions of capital asset pricing model.
2. “When an investor is assumed to use riskless lending and borrowing in
his investment activity, the shape of the efficient frontier transforms into
a straight line.” Illustrate.
3. Write notes on:
(a) Capital market line
(b) Security market line
4. Compare and contrast CML and SML.
5. What is Capital Asset Pricing Model?
6. “CAPM postulates the nature of the relationship between the expected
return and the systematic risk of a security.” Explain.
7. Illustrate graphically how CAPM can be used for assessing whether a
security is underpriced, overpriced or correctly priced.
8. “CAPM can be used to evaluate the pricing of securities.” Discuss.
16
ARBITRAGE PRICING THEORY
(APT)
Modern securities market is a complex phenomenon involving the
simultaneous operation of many factors. The volatility in security prices is
the most visible aspect of the market. However, the search for the underlying
forces which bring about the volatility is an ongoing exercise engaging the
attention of academics and theoreticians for long. Return and risk are two
important characteristics of securities which are interrelated as also changing
over time. An understanding of these two concepts and their interrelationship
is crucial in understanding the pricing of securities in the market. Markowitz
portfolio theory lays the foundation for understanding these concepts. Capital
Asset Pricing Model (CAPM) provides a framework for evaluation of
security pricing based on a single factor, namely, the systematic risk of a
security. In the complex scenario of the modern securities market, a single
factor explanatory model seems to be too narrow in the realistic sense.
Multifactor explanations of security pricing appear to be more appealing
intuitively. Arbitrage Pricing Theory (APT) is such a model which attempts
to explain security pricing behaviour in a multifactor framework.
THE RETURN GENERATING MODEL
The APT model was developed by Stephen Ross in the mid-1970s as an
alternative model to CAPM, in an attempt to address the deficiencies of
CAPM. It is a new and different approach to determine asset prices. The
basic assumption of the theory is that security returns are related to an
unknown number of unknown factors known as risk factors. The theory
assumes that asset returns are generated by a stochastic process which can be
expressed as a linear function of a set of K risk factors (or indices). The APT
postulates that the return on any stock is linearly related to a set of indices.
This linear function can be expressed as:
R = a + b1F1 + b2F2 + … + bkFk + e
Where
R = return on stock
a = the expected return on stock if all factors have zero value
F1, F2, Fk = factors affecting stock return
b1, b2, bk = the sensitivity of stock return to the respective factors
e = random error with mean equal to zero
Multiple factors are expected to have an impact on the return of a security.
These factors may be growth in GDP, inflation, change in interest rate, etc.
These factors are represented in the model by F1, F2, . . . Fk. The impact of
each factor on security returns varies from security to security and from
factor to factor. The impact of a specific factor on a specific security return is
measured by the factor specific beta coefficient, bij.
The APT is thus an estimation of the return that can be expected when returns
are generated by a multi-index model, where sensitivity to changes in each
factor in the model is represented by a factor specific beta coefficient.
FACTORS AFFECTING STOCK RETURN
The APT model is an explanatory model which tries to explain the volatility
in stock prices in terms of multiple factors. But the theory does not specify or
identify the number of factors involved nor the nature of factors involved.
Now the question arises that which are the appropriate factors that determine
security returns? The factors should be able to explain satisfactorily the
variation in security returns. The price of a security is driven by both
macroeconomic factors and microeconomic factors or company specific
factors. The theory does not reveal the identity of the factors. These have to
be determined empirically using historical data of relevant variables.
Moreover, the number and nature of factors is likely to change over time and
across economies.
The process of identifying the relevant factors that have an impact on security
returns involves a difficult operation. Hypotheses regarding feasible factors
have to be formulated on the basis of economic theory for macroeconomic
factors and on the basis of firm specific characteristics for microeconomic
factors. The statistical technique of Factor Analysis using historical data can
be used to identify the factors and estimate their specific impact. The factors
identified in Factor Analysis represent Fj’s in the APT model, while factor
loadings represent the bi’s of the APT model.
Let us assume that Factor Analysis has identified three relevant factors
impacting security returns. These factors have been specified as GDP growth
rate, inflation rate and interest rate with respective factor loadings of 0.08,
1.72 and (−) 0.91 for a particular security. The alpha (a) has a value of 2.36.
The APT model can be formulated as:
R = 2.36 + 0.08F1 + 1.72F2 − 0.91F3
where
F1 = GDP growth rate.
F2 = Inflation rate.
F3 = Interest rate.
EXPECTED RETURN ON STOCK
The return generating model helps in calculating the expected return on any
asset including a security. As the security is a risky asset, the expected return
would be the sum of the risk free return and the risk premium for each risk
factor specified in the return generating model. The expected return may be
mathematically expressed as:
E (R) = λ0 + b1λ1 + b2λ2 + … + bkλk
where
E(R) = Expected stock return.
λ0 = Risk free return.
b1, b2, bk = Sensitivity of stock to respective risk factors.
λ1, λ2, λk = Risk premium for respective risk factors.
This equation represents the core of the APT model. It is basically an
expression of the risk return relationship, similar to CAPM formulation, but
with multiple risk factors. The beta coefficients are the same as those
obtained in the return generating formula. The risk premiums for each factor
(λ1, λ2, λk) are calculated using the following formula:
λ1 = δ1 − rf
λ2 = δ2 − rf
λk = δk − rf
where δ1 is the expected return on stock when it has unit sensitivity to risk
factor 1 and zero sensitivity to all other factors, etc.
δ2, δk are also calculated in a similar fashion.
Thus, risk premium for a factor k is the excess return over risk free return
expected assuming that factor k is the sole risk factor generating or
contributing to the return from the security.
APT equation can be expanded as follows:
E(R) = rf + b1(δ1 − rf) + b2(δ2 − rf) + … + bk(δk − rf)
An Illustration
Let us assume that empirical research has identified two factors as relevant
for generating security returns. These factors are GDP growth rate (factor 1)
and inflation rate (factor 2). The risk premiums associated with each risk
factor has been estimated as:
Factor 1 (λ1) = 5.4 per cent
Factor 2 (λ2) = 3.25 per cent
Government security rate which can be used as the risk free rate (λ0) is
currently 4.25 per cent.
An investor is interested in security A which has the following sensitivities to
the two risk factors.
Sensitivity to Factor 1 (b1) = 0.60
Sensitivity to Factor 2 (b2) = 1.35
The expected return for stock A can be calculated as:
E(R) = λ0 + b1 λ1 + b2 λ2
= 4.25 + (0.60)(5.40) + (1.35)(3.25)
= 4.25 + 3.24 + 4.39
= 11.8 per cent
Let us consider another security B with sensitivities (beta coefficients) of
1.15 and 1.8 to factors 1 and 2, respectively.
The expected return of security B works out as follows:
E(R) = 4.25 + (1.15)(5.4) + (1.8)(3.25)
= 4.25 + 6.21 +5.85
= 16.31 per cent
ASSET PRICING AND ARBITRAGE
The APT model is an asset pricing model which will initiate arbitrage
operations by market participants when there is mispricing of assets in the
market. The model gives the expected rate of return of an asset or security
that is commensurate with its risk. The security price should equal the sum of
all future cash flows discounted at the APT expected rate. A security is
mispriced if its current market price diverges from the price mandated by the
APT model. The mispricing provides an opportunity for arbitrage wherein
market participants will sell the overpriced security and buy the underpriced
security. Such arbitrage operations will eventually correct the mispricing of
securities.
We had earlier considered two securities A and B with expected returns of
11.88 per cent and 16.31 per cent, respectively, as per the APT model. The
current market price of both the securities is ` 30. The prices of the securities
are expected to move up to ` 345 and ` 330, respectively by year end. No
dividend is expected from either of the securities during the year.
With these estimates, we can evaluate whether securities A and B are
correctly priced. The calculations are shown in the table below:
Price Evaluation of Securities
Particulars
Security A
Security B
Sale proceeds of security
345
330
Dividend from security
0
0
Total cash flow
345
330
Discount rate (per cent)
11.88
16.31
Present value of future cash flow
308
284
Current market price
300
300
Cash flow (after one year)
Pricing status
Underpriced Overpriced
Here, security A is underpriced, whereas security B is overpriced. An
arbitrageur would short sell the overpriced security B at the current market
price of ` 300 and use the sale proceeds to buy the underpriced security A for
the same price. Assuming that prices of the securities actually rise to the
levels anticipated, the arbitrage profit that would accrue to the arbitrageur can
be calculated as follows:
Security A
Selling price ` 345
Buying price ` 300
Profit ` 45
Security B
Selling price ` 300
Buying price ` 330
Loss ` 30
Net Profit: ` 45 − ` 30 = ` 15
Continuous arbitrage by market participants will raise the market price of the
underpriced security A and bring down the market price of the overpriced
security B. The mispricing will thus be wiped out through arbitrage trading.
The same situation can be analyzed in an alternative way to evaluate/assess
mispricing of securities.
We have two securities A and B with current market price of ` 300 for both
the securities and expected return of 11.88 per cent for security A and 16.31
per cent for security B. The expected prices of the securities after one year, as
per APT model can be worked out as follows:
E(PA) = 300(1.1188) = ` 336
E(PB) = 300(1.1631) = ` 349
The anticipated prices of the securities at the end of the year are ` 345 and `
330, respectively, for security A and B. It can be seen that the price of
security A is likely to exceed the expected price; hence security A is currently
underpriced. On the contrary, the actual price of security B is not likely to
rise up to the expected price level; hence security B is currently overpriced.
An arbitrageur will accordingly short sell the overpriced security B at the
current market price and buy the underpriced security A for the same price.
The profit from the arbitrage trading will be as follows:
Profit from security A: 345 − 300 = ` 45
Profit from security B: 300 − 330 = (−) ` 30
Net profit: 45 − 30 = ` 15
CONCLUSION ON APT
The APT model is based on the principle that in an efficient security market
there will be no arbitrage opportunities. Such a market will follow the ‘Law
of One Price’ which implies that two assets or securities which are equivalent
in all economically relevant aspects must have the same market price. APT
model helps to identify mispriced securities and thereby helps in initiating
arbitrage operations to ultimately lead to correct pricing of securities in the
market.
This is a new model of asset pricing, which is developed as an alternative to
CAPM. The theory proposes that a set of multiple factors is needed to explain
security returns and thereby security pricing. But the theory does not specify
or identify the factor structure that affects security returns. Identifying the
factor structure is a serious challenge in the application of APT model for
asset pricing. Another serious problem with APT model concerns the stability
of the factor structure over time. Are the factors stable over time? Does the
same set of factors explain security returns and prices at different points in
time? Only empirical tests and research studies can answer these questions.
APT AND CAPM
APT was developed as an alternative to CAPM. Hence, it is important to
know the similarities and differences between APT and CAPM.
Both the models attempt to establish the relationship between risk factors and
the expected return on securities. The relationship in both the cases is
expressed as a linear function. In both the models, the expected return is
calculated as the sum of the risk free return and risk premium which depends
upon the sensitivity of the stock to the risk factors. Thus, the formulation of
both the models is similar.
The chief differentiating feature is the number and nature of risk factors used
in the two models. CAPM is a single factor model. Further, the single risk
factor used in CAPM is well defined and it is the systematic risk of the
security measured by Beta. The risk premium in CAPM is the excess of the
Market portfolio return over the risk free return. However, there is a practical
difficulty in identifying the Market portfolio and calculating the return of the
Market portfolio. In APT model, the number and nature of risk factors are
unknown. The model does not specify in advance the risk factors to be
considered. They have to be determined empirically.
The CAPM is a statistical model with well-defined parameters, whereas the
APT is an explanatory model with undefined parameters that have to be
identified and defined before the model is used. By limiting itself to a single
risk factor, CAPM may fail to explain fully the complex nature of security
pricing. On the contrary, APT model assumes flexibility to incorporate
multifactors in the model to account for the diverse factors at play in the
securities market.
SOLVED EXAMPLES
Example 1 Consider the following data for two risk factors and two securities
(M and N):
λ0 = 8 per cent
λ1 = 4.5 per cent
λ2 = 8.2 per cent
bM1 = 0.76
bM2 = 1.90
bN1 = 1.72
bN2 = 2.45
Security M is currently priced at ` 225; security N is currently priced at ` 150.
Anticipated prices of the securities at year end are ` 275 and ` 175,
respectively.
(a) Compute expected return of both securities.
(b) What is the expected price of each security one year from now?
(c) Evaluate whether the securities are correctly priced.
Solution
(a) Expected return of a security can be calculated using APT formula:
E(R) = λ0 + b1λ1 + b2λ2
Security M: 8.00 + (0.76)(4.5) + (1.9)(3.2)
= 8.00 + 3.42 + 6.08 = 17.5 per cent
Security N: 8.00 + (1.72)(4.5) + (2.45)(3.2)
= 8.00 + 7.74 + 7.84 = 23.5 per cent
(b) Expected price of security after one year can be calculated based on the
expected return:
Security M: 225(1 + 0.175) = ` 264.38
Security N: 150(1 + 0.2358) = ` 185.37
(c) Evaluation of pricing can be done by comparing the expected price based
on risk factors and using APT model and the actual anticipated year end
price:
Security M
Expected price (theoretical price): ` 264.38
Anticipated actual price: ` 275
As actual price is expected to exceed the theoretical price, the security is
attractive; it is currently underpriced.
Security N
Expected price (theoretical price): ` 185.37
Anticipated actual price: ` 175
As the actual price is not expected to move up to the theoretical price or
expected price, the security is not attractive; it is currently overpriced.
Example 2 Consider the following data for two risk factors and two securities
(C and D):
λ0 = 4.25 per cent
λ1 = 5.5 per cent
λ2 = 3.8 per cent
bC1 = 1.12
bC2 = 1.74
bD1 = 0.92
bD2 = 2.30
Security C is currently priced at ` 340
Security D is currently priced at ` 270
During the year the securities are expected to pay dividends of ` 4.00 and `
5.50 per share, respectively. The year-end prices are anticipated to be ` 375
for security C and ` 320 for security D.
(a) Compute the expected return of both securities.
(b) Evaluate whether the securities are correctly priced.
Example 3 Consider the following data regarding three risk factors and three
securities (X, Y and Z).
Factor Loadings
Security
F1
F2
F3
X
1.12
(−)0.56
0.63
Y
0.85
0.74
0.47
Z
1.30
(−)0.24
1.23
Risk premium associated with the risk factors are:
λ1 = 4.75 per cent λ2 = 2.30 per cent λ3 = (−) 1.7 per cent
Current market price and the anticipated future price of the three securities
are:
Security Prices
Security
Current price
Future price
X
410
430
Y
145
175
Z
570
620
(a) Compute the expected return of the three securities, assuming risk free
return of 5.5 per cent.
(b) Evaluate whether the securities are correctly priced.
(b) Evaluation of security pricing is done by comparing the current market
price of the security with the present value of future cash flows
discounted at the APT expected return rate.
Particulars
Security X
Security Y
Security Z
Future cash flow (Sale proceeds of
security)
430
175
620
Discount rate (APT expected return)
8.46
10.44
9.04
Present value of future cash flow
396
158
569
Current market price of security
Pricing status
410
145
570
Overpriced
Underpriced
Correctly
priced
Example 4 Three securities (X, Y and Z) and two common risk factors have
the following relationship:
E(Rx) = (0.9)λ1 + (1.2)λ2
E(Ry) = (0.5)λ1 + (1.35)λ2
E(Rz) = (0.42)λ1 + (1.15)λ2
The risk premiums for factor 1 and factor 2 have been estimated as:
λ1 = 7 per cent
λ2 = 3.8 per cent
risk free rate = 4.5 per cent
The three securities are currently priced at the same level with selling price of
` 335 each. None of the securities are expected to pay any dividend during the
year.
The selling price of the securities forecasted for the year end are:
X: ` 375
Y: ` 385
Z: ` 380
(a) Compute the expected prices of the three securities at the year-end
based on their risk profile.
(b) Evaluate whether the securities are correctly priced.
(c) Explain the arbitrage trading strategy to be used in case of any
mispricing of the securities.
(d) Calculate the arbitrage profit.
(b) Pricing of securities can be evaluated by comparing the future forecasted
price and the price expected on the basis of risk profile of securities
Securities
Forecasted future price
Expected year end price
Pricing status
X
375
386
Overpriced
Y
385
379
Underpriced
Z
380
375
Underpriced
(c) Arbitrage trading strategy
The general principle of arbitrage trading is: ‘Buy underpriced assets
and sell overpriced assets.’
Security X is overpriced; securities Y and Z are underpriced. The
strategy here would be to short sell 2 numbers of security X for ` 670 (`
335 × 2) and use the sale proceeds to buy one security Y for ` 335 and
one security Z for ` 335.
(d) Calculation of arbitrage profit
Security X
Short sale of 2 numbers of security X will have to be covered at year end
by buying 2 numbers of security X at ` 375 per security (the forecasted
future price).
Loss in the transaction
Selling price (2 shares × ` 335): ` 670
Buying price (2 shares × ` 375): ` 750
Loss: ` 80
Security Y
Selling price (forecasted future price): ` 385
Buying price: ` 335
Profit: ` 50
Security Z
Selling price (forecasted future price): ` 380
Buying price: ` 335
Profit: ` 45
Net Profit from arbitrage trading: ` 50 + ` 45 − ` 80 = ` 15
EXERCISES
1. Consider the following data for two risk factors and two securities (A
and B):
λ0 = 6.15 per cent
λ1 = 3.25 per cent
λ2 = 4.5 per cent
bA1 = 1.34
bA2 = 0.85
bB1 = 0.24
bB2 = 1.74
Security A is currently selling for ` 830 and the forecasted year end price
of the security is ` 950.
Security B is currently selling for ` 160 and the forecasted year end price
of the security is ` 205.
(d) Compute expected return of securities A and B.
(e) What is the expected price of the securities one year from now?
(f) Evaluate whether the securities are correctly priced.
2. Consider the following data for two risk factors and two securities (M
and N):
λ0 = 5.00 per cent
λ1 = 6.25 per cent
λ2 = 2.85 per cent
bM1 = 2.05
bM2 = 0.58
bN1 = 1.45
bN2 = 0.98
Security M is currently priced at ` 225
Security N is currently priced at ` 530
During the year the securities are expected to pay dividends of ` 6.25
and ` 8.50 per share respectively. The year-end prices of the securities
forecasted are: ` 256 (Security M) and ` 650 (Security N).
(c) Compute the expected return of the securities
(d) Evaluate the pricing of the securities.
3. Consider the following data regarding three risk factors and three
securities (P, Q and R).
Factor Loadings
Security
F1
F2
F3
P
0.68
1.23
(−) 0.82
Q
1.47
0.88
1.24
R
(−) 0.56
1.46
0.73
Risk premium associated with the risk factors are:
λ1 = 3.5 per cent λ2 = 6.12 per cent λ3 = 2.17 per cent
Current market price and the anticipated future price of the three
securities are:
Security Prices
Security
Current price
Future price
P
84
120
Q
315
355
R
436
460
(c) Compute the expected return of the securities, assuming risk free
return of 8 per cent.
(d) Evaluate the pricing of securities.
4. Three securities (A, B and C) and two common risk factors have the
following relationship:
E(RA) = (1.33)λ1 + (0.76)λ2
E(RB) = (2.5)λ1 + (1.3)λ2
E(RC) = (0.38)λ1 + (1.42)λ2
The risk premiums for factor 1 and factor 2 have been estimated as:
λ1 = 5.35 per cent λ2 = 4.75 per cent risk free rate = 7.25 per cent
The three securities are currently selling for the same price of ` 215.
None of the securities are expected to pay any dividend during the year.
The selling price of the securities forecasted for the year end are:
A: ` 255
B: ` 260
C: ` 265
(e) Compute the expected prices of the securities at the year-end based
on their risk profile.
(f) Evaluate whether the securities are correctly priced.
(g) Explain the arbitrage trading strategy to be used in case of any
mispricing of the securities.
(h) Calculate the arbitrage profit.
REVIEW QUESTIONS
1. Explain the return generating process in APT.
2. “APT is a multifactor model of asset pricing”. Explain.
3. What are the risk factors in APT model? How are they determined?
4. How is expected return on stock calculated as per APT model?
5. How is mispricing of securities identified using APT model?
6. Evaluate the usefulness of APT model for asset pricing.
7. What is Arbitrage Pricing theory? What are its similarities and
differences relative to CAPM?
17
PORTFOLIO REVISION
In portfolio management, the maximum emphasis is placed on portfolio
analysis and selection which leads to the construction of the optimal
portfolio. Very little discussion is seen on portfolio revision which is as
important as portfolio analysis and selection.
The financial markets are continually changing. In this dynamic environment,
a portfolio that was optimal when constructed may not continue to be optimal
with the passage of time. It may have to be revised periodically so as to
ensure that it continues to be optimal.
NEED FOR REVISION
The primary factor necessitating portfolio revision is changes in the financial
markets since the creation of the portfolio. The need for portfolio revision
may arise because of some investor related factors also. These factors may be
listed as:
1. Availability of additional funds for investment
2. Change in risk tolerance
3. Change in the investment goals
4. Need to liquidate a part of the portfolio to provide funds for some
alternative use
The portfolio needs to be revised to accommodate the changes in the
investor’s position.
Thus, the need for portfolio revision may arise from changes in the financial
market or changes in the investor’s position, namely his financial status and
preferences.
MEANING OF PORTFOLIO REVISION
A portfolio is a mix of securities selected from a vast universe of securities.
Two variables determine the composition of a portfolio; the first is the
securities included in the portfolio and the second is the proportion of total
funds invested in each security.
Portfolio revision involves changing the existing mix of securities. This may
be effected either by changing the securities currently included in the
portfolio or by altering the proportion of funds invested in the securities. New
securities may be added to the portfolio or some of the existing securities
may be removed from the portfolio. Portfolio revision thus leads to purchases
and sales of securities. The objective of portfolio revision is the same as the
objective of portfolio selection, i.e. maximising the return for a given level of
risk or minimising the risk for a given level of return. The ultimate aim of
portfolio revision is maximisation of returns and minimisation of risk.
CONSTRAINTS IN PORTFOLIO REVISION
Portfolio revision is the process of adjusting the existing portfolio in
accordance with the changes in financial markets and the investor’s position
so as to ensure maximum return from the portfolio with the minimum of risk.
Portfolio revision or adjustment necessitates purchase and sale of securities.
The practice of portfolio adjustment involving purchase and sale of securities
gives rise to certain problems which act as constraints in portfolio revision.
Some of these are discussed below:
Transaction Cost
Buying and selling of securities involve transaction costs such as commission
and brokerage. Frequent buying and selling of securities for portfolio revision
may push up transaction costs thereby reducing the gains from portfolio
revision. Hence, the transaction costs involved in portfolio revision may act
as a constraint to timely revision of portfolio.
Taxes
Tax is payable on the capital gains arising from sale of securities. Usually,
long-term capital gains are taxed at a lower rate than short-term capital gains.
To qualify as long- term capital gain, a security must be held by an investor
for a period of not less than 12 months before sale. Frequent sales of
securities in the course of periodic portfolio revision or adjustment will result
in short-term capital gains which would be taxed at a higher rate compared to
long-term capital gains. The higher tax on short-term capital gains may act as
a constraint to frequent portfolio revisions.
Statutory Stipulations
The largest portfolios in every country are managed by investment companies
and mutual funds. These institutional investors are normally governed by
certain statutory stipulations regarding their investment activity. These
stipulations often act as constraints in timely portfolio revision.
Intrinsic Difficulty
Portfolio revision is a difficult and time consuming exercise. The
methodology to be followed for portfolio revision is also not clearly
established. Different approaches may be adopted for the purpose. The
difficulty of carrying out portfolio revision itself may act as a constraint to
portfolio revision.
PORTFOLIO REVISION STRATEGIES
Two different strategies may be adopted for portfolio revision, namely an
active revision strategy and a passive revision strategy. The choice of the
strategy would depend on the investor’s objectives, skill, resources and time.
Active revision strategy involves frequent and sometimes substantial
adjustments to the portfolio. Investors who undertake active revision strategy
believe that security markets are not continuously efficient. They believe that
securities can be mispriced at times giving an opportunity for earning excess
returns through trading in them. Moreover, they believe that different
investors have divergent or heterogeneous expectations regarding the risk and
return of securities in the market. The practitioners of active revision strategy
are confident of developing better estimates of the true risk and return of
securities than the rest of the market. They hope to use their better estimates
to generate excess returns. Thus, the objective of active revision strategy is to
beat the market.
Active portfolio revision is essentially carrying out portfolio analysis and
portfolio selection all over again. It is based on an analysis of the
fundamental factors affecting the economy, industry and company as also the
technical factors like demand and supply. Consequently, the time, skill and
resources required for implementing active revision strategy will be much
higher. The frequency of trading is likely to be much higher under active
revision strategy resulting in higher transaction costs.
Passive revision strategy, in contrast, involves only minor and infrequent
adjustment to the portfolio over time. The practitioners of passive revision
strategy believe in market efficiency and homogeneity of expectation among
investors. They find little incentive for actively trading and revising
portfolios periodically.
Under passive revision strategy, adjustment to the portfolio is carried out
according to certain predetermined rules and procedures designated as
formula plans. These formula plans help the investor to adjust his portfolio
according to changes in the securities market.
FORMULA PLANS
In the market, the prices of securities fluctuate. Ideally, investors should buy
when prices are low and sell when prices are high. If portfolio revision is
done according to this principle, investors would be able to benefit from the
price fluctuations in the securities market. But investors are hesitant to buy
when prices are low either expecting that prices will fall further lower or
fearing that prices would not move upwards again. Similarly, when prices are
high, investors hesitate to sell because they feel that prices may rise further
and they may be able to realise larger profits.
Thus, left to themselves, investors would not be acting in the way required to
benefit from price fluctuations. Hence, certain mechanical revision
techniques or procedures have been developed to enable the investors to
benefit from price fluctuations in the market by buying stocks when prices
are low and selling them when prices are high. These techniques are referred
to as formula plans.
Formula plans represent an attempt to exploit the price fluctuations in the
market and make them a source of profit to the investor. They make the
decisions on timings of buying and selling securities automatic and eliminate
the emotions surrounding the timing decisions. Formula plans consist of
predetermined rules regarding when to buy or sell and how much to buy or
sell. These predetermined rules call for specified actions when there are
changes in the securities market.
The use of formula plans demands that the investor divide his investment
funds into two portfolios, one aggressive and the other conservative or
defensive. The aggressive portfolio usually consists of equity shares while the
defensive portfolio consists of bonds and debentures. The formula plans
specify predetermined rules for the transfer of funds from the aggressive
portfolio to the defensive portfolio and vice versa. These rules enable the
investor to automatically sell shares when their prices are rising and buy
shares when their prices are falling.
There are different formula plans for implementing passive portfolio revision.
Let us discuss some of the important ones.
Constant Rupee Value Plan
This is one of the most popular or commonly used formula plans. In this plan,
the investor constructs two portfolios, one aggressive, consisting of equity
shares and the other, defensive, consisting of bonds and debentures. The
purpose of this plan is to keep the value of the aggressive portfolio constant,
i.e. at the original amount invested in the aggressive portfolio.
As share prices fluctuate, the value of the aggressive portfolio keeps
changing. When share prices are increasing, the total value of the aggressive
portfolio increases. The investor has to sell some of the shares from his
portfolio to bring down the total value of the aggressive portfolio to the level
of his original investment in it. The sale proceeds will be invested in the
defensive portfolio by buying bonds and debentures.
On the contrary, when share prices are falling, the total value of the
aggressive portfolio would also decline. To keep the total value of the
aggressive portfolio at its original level, the investor has to buy some shares
from the market to be included in his portfolio. For this purpose, a part of the
defensive portfolio will be liquidated to raise the money needed to buy
additional shares.
Under this plan, the investor is effectively transferring funds from the
aggressive portfolio to the defensive portfolio and thereby booking profit
when share prices are increasing. Funds are transferred from the defensive
portfolio to the aggressive portfolio when share prices are low. Thus, the plan
helps the investor to buy shares when their prices are low and sell them when
their prices are high.
In order to implement this plan, the investor has to decide the action points,
i.e. when he should make the transfer of funds to keep the rupee value of the
aggressive portfolio constant. These action points, or revision points, should
be predetermined and should be chosen carefully. The revision points have a
significant effect on the returns of the investor. For instance, the revision
points may be predetermined as 10 per cent, 15 per cent, 20 per cent etc.
above or below the original investment in the aggressive portfolio. If the
revision points are too close, the number of transactions would be more and
the transaction costs would increase reducing the benefits of revision. If the
revision points are set too far apart, it may not be possible to profit from the
price fluctuations occurring between these revision points.
We can understand the working of the ‘constant rupee value plan’ by
considering an example. Let us consider an investor who has ` 1,00,000 for
investment. He decides to invest ` 50,000 in an aggressive portfolio of equity
shares and the remaining ` 50,000 in a defensive portfolio of bonds and
debentures. He purchases 1250 shares selling at ` 40 per share for his
aggressive portfolio. The revision points are fixed as 20 per cent above or
below the original investment of ` 50,000.
After the construction of the portfolios, the share price will fluctuate. If the
price of the share increases to ` 45, the value of the aggressive portfolio
increases to ` 56,250 (that is, 1250 × ` 45). Since the revision points are fixed
at 20 per cent above or below the original investment, the investor will act
only when the value of the aggressive portfolio increases to ` 60,000 or falls
to ` 40,000. If the price of the share increases to ` 48 or above, the value of
the aggressive portfolio will exceed ` 60,000. Let us suppose that the price of
the share increases to ` 50, the value of the aggressive portfolio will be `
62,500. The investor will sell shares worth ` 12,500 (that is 250 shares at ` 50
per share) and transfer the amount to the defensive portfolio by buying bonds
for ` 12,500. The value of the aggressive and defensive portfolios would now
be ` 50,000 and ` 62,500 respectively. The aggressive portfolio now has only
1000 shares valued at ` 50 per share.
Let us now suppose that the share price falls to ` 40 per share. The value of
the aggressive portfolio would then be ` 40,000 (i.e. 1000 shares × ` 40)
which is 20 per cent less than the original investment. The investor now has
to buy shares worth ` 10,000 (that is, 250 shares at ` 40 per share) to bring the
value of the aggressive portfolio to its original level of ` 50,000. The money
required for buying the shares will be raised by selling bonds from the
defensive portfolio.
The two portfolios now will have values of ` 50,000 (aggressive) and `
52,500 (i.e. ` 62,500 − ` 10,000) (defensive), aggregating to ` 1,02,500. It
may be recalled that the investor started with ` 1,00,000 as investment in the
two portfolios.
Thus, when the ‘constant rupee value plan’ is being implemented, funds will
be transferred from one portfolio to the other, whenever the value of the
aggressive portfolio increases or declines to the predetermined levels.
Constant Ratio Plan
This is a variation of the constant rupee value plan. Here again the investor
would construct two portfolios, one aggressive and the other defensive with
his investment funds. The ratio between the investments in the aggressive
portfolio and the defensive portfolio would be predetermined such as 1:1 or
1.5:1 etc. The purpose of this plan is to keep this ratio constant by readjusting
the two portfolios when share prices fluctuate from time to time. For this
purpose, a revision point will also have to be predetermined. The revision
points may be fixed as ± 0.10 for example. This means that when the ratio
between the values of the aggressive portfolio and the defensive portfolio
moves up by 0.10 points or moves down by 0.10 points, the portfolios would
be adjusted by transfer of funds from one to the other.
Let us assume that an investor starts with ` 20,000, investing ` 10,000 each in
the aggressive portfolio and the defensive portfolio. The initial ratio is then
1:1. He has predetermined the revision points as ±0.20. As share price
increases the value of the aggressive portfolio would rise. When the value of
the aggressive portfolio rises to ` 12,000, the ratio becomes 1.2:1 (i.e. `
12,000 : ` 10,000). Shares worth ` 1,000 will be sold and the amount
transferred to the defensive portfolio by buying bonds. Now, the value of
both the portfolios would be ` 11,000 and the ratio would become 1:1.
Now let us assume that the share prices are falling. The value of the
aggressive portfolio would start declining. If, for instance, the value declines
to ` 8,500, the ratio becomes 0.77:1 (i.e. ` 8,500 : ` 11,000). The ratio has
declined by more than 0.20 points. The investor now has to make the value of
both portfolios equal. He has to buy shares worth ` 1,250 by selling bonds for
an equivalent amount from his defensive portfolio. Now the value of the
aggressive portfolio increases by ` 1,250 and that of the defensive portfolio
decreases by ` 1,250. The values of both portfolios become ` 9,750 and the
ratio becomes 1:1.
The adjustment of portfolios is done periodically in this manner.
Dollar Cost Averaging
This is another method of passive portfolio revision. This is, however,
different from the two formula plans discussed above. All formula plans
assume that stock prices fluctuate up and down in cycles. Dollar cost
averaging utilises this cyclic movement in share prices to construct a
portfolio at low cost.
The plan stipulates that the investor invest a constant sum, such as ` 5,000, `
10,000, etc. in a specified share or portfolio of shares regularly at periodical
intervals, such as a month, two months, a quarter, etc. regardless of the price
of the shares at the time of investment. This periodic investment is to be
continued over a fairly long period to cover a complete cycle of share price
movements.
If the plan is implemented over a complete cycle of stock prices, the investor
will obtain his shares at a lower average cost per share than the average price
prevailing in the market over the period. This occurs because more shares
would be purchased at lower prices than at higher prices.
The dollar cost averaging is really a technique of building up a portfolio over
a period of time. The plan does not envisage withdrawal of funds from the
portfolio in between. When a large portfolio has been built up over a
complete cycle of share price movements, the investor may switch over to
one of the other formula plans for its subsequent revision. The dollar cost
averaging is specially suited to investors who have periodic sums to invest.
The various formula plans attempt to make portfolio revision a simple and
almost mechanical exercise enabling the investor to automatically buy shares
when their prices are low and sell them when their prices are high. But
formula plans have their limitations. By their very nature they are inflexible.
Further, these plans do not indicate which securities from the portfolio are to
be sold and which securities are to be bought to be included in the portfolio.
Only active portfolio revision can provide answers to these questions.
REVIEW QUESTIONS
1. What is meant by portfolio revision?
2. What factors necessitate portfolio revision?
3. Describe the major constraints in portfolio revision.
4. Distinguish between active revision strategy and passive revision
strategy.
5. What are formula plans? Explain the constant rupee value plan with
examples.
6. Compare and contrast constant rupee value plan and constant ratio plan.
7. “Dollar cost averaging utilises the cyclical movement in share prices to
construct a portfolio at low cost.” Explain.
8. “Formula plans attempt to make portfolio revision a simple and almost
mechanical exercise.” Discuss.
18
PORTFOLIO EVALUATION
Portfolio evaluation is the last step in the process of portfolio management.
Portfolio analysis, selection and revision are undertaken with the objective of
maximising returns and minimising risk. Portfolio evaluation is the stage
where we examine to what extent the objective has been achieved. Through
portfolio evaluation the investor tries to find out how well the portfolio has
performed. The portfolio of securities held by an investor is the result of his
investment decisions. Portfolio evaluation is really a study of the impact of
such decisions. Without portfolio evaluation, portfolio management would be
incomplete.
Two decades ago portfolio evaluation was not considered as an integral part
of portfolio management. It has evolved as an important aspect of portfolio
management over the last two decades. Moreover, the evaluation process
itself has changed from crude return calculations to rather detailed
explorations of risk and return and the sources of each.
NEED FOR EVALUATION
Investment may be carried out by individuals on their own. The funds
available with individual investors may not be large enough to create a well
diversified portfolio of securities. Moreover, the time, skill and other
resources at the disposal of individual investors may not be sufficient to
manage the portfolio professionally. Institutional investors such as mutual
funds and investment companies are better equipped to create and manage
well diversified portfolios in a professional fashion. Hence, small investors
may prefer to entrust their funds with mutual funds or investment companies
to avail the benefits of their professional services and thereby achieve
maximum return with minimum risk and effort.
Evaluation is an appraisal of performance. Whether the investment activity is
carried out by individual investors themselves or through mutual funds and
investment companies, different situations arise where evaluation of
performance becomes imperative. These situations are discussed below:
Self Evaluation
Where individual investors undertake the investment activity on their own,
the investment decisions are taken by them. They construct and manage their
own portfolio of securities. In such a situation, an investor would like to
evaluate the performance of his portfolio in order to identify the mistakes
committed by him. This self evaluation will enable him to improve his skills
and achieve better performance in future.
Evaluation of Portfolio Managers
A mutual fund or investment company usually creates different portfolios
with different objectives aimed at different sets of investors. Each such
portfolio may be entrusted to different professional portfolio managers who
are responsible for the investment decisions regarding the portfolio entrusted
to each of them. In such a situation, the organisation would like to evaluate
the performance of each portfolio so as to compare the performance of
different portfolio managers.
Evaluation of Mutual Funds
In India, at present, there are many mutual funds as also investment
companies operating both in the public sector as well as in the private sector.
These compete with each other for mobilising the investment funds with
individual investors and other organisations by offering attractive returns,
minimum risk, high safety and prompt liquidity. Investors and organisations
desirous of placing their funds with these mutual funds would like to know
the comparative performance of each so as to select the best mutual fund or
investment company. For this, evaluation of the performance of mutual funds
and their portfolios becomes necessary.
EVALUATION PERSPECTIVE
A portfolio comprises several individual securities. In the building up of the
portfolio several transactions of purchase and sale of securities take place.
Thus, several transactions in several securities are needed to create and revise
a portfolio of securities. Hence, the evaluation may be carried out from
different perspectives or viewpoints such as a transactions view, security
view or portfolio view.
Transaction View
An investor may attempt to evaluate every transaction of purchase and sale of
securities. Whenever a security is bought or sold, the transaction is evaluated
as regards its correctness and profitability.
Security View
Each security included in the portfolio has been purchased at a particular
price. At the end of the holding period, the market price of the security may
be higher or lower than its cost price or purchase price. Further, during the
holding period, interest or dividend might have been received in respect of
the security. Thus, it may be possible to evaluate the profitability of holding
each security separately. This is evaluation from the security viewpoint.
Portfolio View
A portfolio is not a simple aggregation of a random group of securities. It is a
combination of carefully selected securities, combined in a specific way so as
to reduce the risk of investment to the minimum. An investor may attempt to
evaluate the performance of the portfolio as a whole without examining the
performance of individual securities within the portfolio. This is evaluation
from the portfolio view.
Though evaluation may be attempted at the transaction level, or the security
level, such evaluations would be incomplete, inadequate and often
misleading. Investment is an activity involving risk. Proper evaluation of the
investment activity must, therefore, consider return along with risk involved.
But risk is best defined at the portfolio level and not at the security level or
transaction level. Hence, the best perspective for evaluation is the portfolio
view.
MEANING OF PORTFOLIO EVALUATION
Portfolio evaluation refers to the evaluation of the performance of the
portfolio. It is essentially the process of comparing the return earned on a
portfolio with the return earned on one or more other portfolios or on a
benchmark portfolio. Portfolio evaluation essentially comprises two
functions, performance measurement and performance evaluation.
Performance measurement is an accounting function which measures the
return earned on a portfolio during the holding period or investment period.
Performance evaluation, on the other hand, addresses such issues as whether
the performance was superior or inferior, whether the performance was due to
skill or luck, etc.
While evaluating the performance of a portfolio, the return earned on the
portfolio has to be evaluated in the context of the risk associated with that
portfolio. One approach would be to group portfolios into equivalent risk
classes and then compare returns of portfolios within each risk category. An
alternative approach would be to specifically adjust the return for the
riskiness of the portfolio by developing risk adjusted return measures and use
these for evaluating portfolios across differing risk levels.
Measuring Portfolio Return
The first step in portfolio evaluation is calculation of the rate of return earned
over the holding period. Return may be defined to include changes in the
value of the portfolio over the holding period plus any income earned over
the period. However, in the case of mutual funds, during the holding period,
cash inflows into the fund and cash withdrawals from the fund may occur.
The unit-value method may be used to calculate return in this case.
The one period rate of return, r, for a mutual fund may then be defined as the
change in the per unit net asset value (NAV), plus its per unit cash
disbursements (D) and per unit capital gains disbursements (C) such as bonus
shares. It may be calculated as:
where
NAVt = NAV per unit at the end of the holding period.
NAVt − 1 = NAV per unit at the beginning of the holding period.
Dt = Cash disbursements per unit during the holding period.
Ct = Capital gains disbursements per unit during the holding period.
This formula gives the holding period yield or rate of return earned on a
portfolio. This may be expressed as a percentage.
The rate of return earned by different mutual funds or mutual fund schemes
may be calculated and compared with the rate of return earned by a
representative stock market index which can be used as a benchmark for
comparative evaluation. The mutual funds may also be ranked in descending
order of their rates of return. But such straight forward rates of return
comparison may be incomplete and sometimes even misleading. The
differential return earned by mutual funds could be due entirely to the
differential risk exposure of the funds. Hence, the returns have to be adjusted
for risk before making any comparison.
Risk Adjusted Returns
One obvious method of adjusting for risk is to look at the reward per unit of
risk. We know that investment in shares is risky. Risk free rate of interest is
the return that an investor can earn on a riskless security, i.e. without bearing
any risk. The return earned over and above the risk free rate is the risk
premium that is the reward for bearing risk. If this risk premium is divided by
a measure of risk, we get the risk premium per unit of risk. Thus, the reward
per unit of risk for different portfolios or mutual funds may be calculated and
the funds may be ranked in descending order of the ratio. A higher ratio
indicates better performance.
Two methods of measuring the reward per unit of risk have been proposed by
William Sharpe and Jack Treynor respectively in their pioneering work on
evaluation of portfolio performance.
Sharpe Ratio
The performance measure developed by William Sharpe is referred to as the
Sharpe ratio or the reward to variability ratio. It is the ratio of the reward or
risk premium to the variability of return or risk as measured by the standard
deviation of return. The formula for calculating Sharpe ratio may be stated as:
Treynor Ratio
The performance measure developed by Jack Treynor is referred to as
Treynor ratio or reward to volatility ratio. It is the ratio of the reward or risk
premium to the volatility of return as measured by the portfolio beta. The
formula for calculating Treynor ratio may be stated as:
To understand the calculation of the two ratios let us consider an example.
The return and risk figures of two mutual funds and the stock market index
are given in the table.
Fund
Return (per cent)
Standard deviation (per cent)
Beta
A
12
18
0.7
Z
19
25
1.3
M (Market index)
15
20
1.0
The risk free rate of return is 7 per cent.
According to Treynor’s performance measure also, fund Z has performed
better and fund A has performed worse than the benchmark.
Both the ratios are relative measures of performance because they relate the
return to the risk involved. However, they differ in the measure of risk used
for the purpose. Sharpe uses the total risk as measured by standard deviation,
while Treynor employs the systematic risk as measured by the beta
coefficient. In a fully diversified portfolio, all unsystematic risk would be
diversified away and the relevant measure of risk would be the beta
coefficient. For such a portfolio, Treynor ratio would be the appropriate
measure of performance evaluation. For a portfolio that is not so well
diversified, the Sharpe ratio using the total risk measure would be the
appropriate performance measure.
DIFFERENTIAL RETURN
Another type of risk adjusted performance measure has been developed by
Michael Jensen and is referred to as the Jensen measure or ratio. This ratio
attempts to measure the differential between the actual return earned on a
portfolio and the return expected from the portfolio given its level of risk.
The CAPM model is used to calculate the expected return on a portfolio. It
indicates the return that a portfolio should earn for its given level of risk. The
difference between the return actually earned on a portfolio and the return
expected from the portfolio is a measure of the excess return or differential
return that has been earned over and above what is mandated for its level of
systematic risk. The differential return gives an indication of the portfolio
manager’s predictive ability or managerial skills.
Using the CAPM model, the expected return of the portfolio can be
calculated as follows:
E(Rp) = Rf + βp (Rm − Rf)
where
E(Rp) = Expected portfolio return.
Rf = Risk free rate.
Rm = Return on market index.
βp = Systematic risk of the portfolio.
The differential return is calculated as follows:
αp = Rp − E(Rp)
where
αp = Differential return earned.
Rp = Actual return earned on the portfolio.
E(Rp) = Expected return.
Thus, αp represents the difference between actual return and expected return.
If αp has a positive value, it indicates that superior return has been earned due
to superior management skills. When αp = 0, it indicates neutral performance.
It means that the portfolio manager has done just as well as an unmanaged
randomly selected portfolio with a buy and hold strategy. A negative value of
αp indicates that the portfolio’s performance has been worse than that of the
market or a randomly selected portfolio of equivalent risk.
The alpha value in Jensen measure can be tested for its degree of significance
from a value of zero by statistical methods. This means, an analyst can
determine whether the differential return could have occurred by chance or
whether it is significantly different from zero in a statistical sense.
Let us consider funds A and Z. The actual returns realised from the two funds
are 12 per cent and 19 per cent respectively with beta coefficients being 0.7
and 1.3 respectively. The market return is 15 per cent and the risk free rate is
7 per cent.
The expected return on the two funds can be calculated as shown below:
Fund A: E(Rp) = 7 + 0.7(15 − 7) = 12.6
Fund Z: E(Rp) = 7 + 1.3 (15 − 7) = 17.4
The differential return or alpha value is shown below:
Fund A: αp = 12 − 12.6 = −0.6
Fund Z: αp = 19 − 17.4 = 1.6
The negative value of alpha for fund A indicates that its performance has
been inferior. The positive value of alpha for fund Z indicates that its
performance has been superior, presumably due to the superior management
skills of its portfolio managers.
DECOMPOSITION OF PERFORMANCE
The performance measures discussed so far assess the overall performance of
a portfolio or fund. Eugene Fama has provided an analytical framework that
allows a detailed breakdown of a fund’s performance into the source or
components of performance. This is known as the Fama decomposition of
total return.
The total return on a portfolio can be firstly divided into two components,
namely risk free return and the excess return. Thus,
Total return = Risk free return + Excess return
The excess return arises from different factors or sources, such as risk bearing
and stock selection. Hence the excess return, in turn, may be decomposed
into two components, namely risk premium or reward for bearing risk and
return from stock selection known as return from stock selectivity. Thus,
Excess return= Risk premium + Return from stock selection
The risk of a security is of two types: systematic risk and unsystematic risk or
diversifiable risk. When a portfolio of securities is created, most of the
unsystematic risk or diversifiable risk would disappear. But, in practice, no
portfolio would be fully diversified. Hence, a portfolio would have both
systematic risk and a small amount of diversifiable risk. Hence, the risk
premium can be decomposed into two components, namely return for bearing
systematic risk (market risk) and return for bearing diversifiable risk. Thus,
Risk premium = Return for bearing systematic risk + Return for bearing
diversifiable risk
Thus, the total return on a portfolio can be decomposed into four
components.
Return on portfolio = Riskless rate + Return from market risk +
Return from diversifiable risk + Return from pure selectivity
This may be represented as:
Rp = Rf + R1 + R2 + R3
Each component can be calculated. The risk free rate of return (Rf) is the
return available on a riskless asset such as the government security.
The return from market risk (R1) is calculated as:
R1 = βp (Rm − Rf)
where
Rm = Return on the market index.
The return from diversifiable risk (R2) is calculated as:
R2 = [(σp/σm) − βp] (Rm − Rf)
where
σp = Portfolio standard deviation.
σm = Standard deviation of the market index.
The return from pure selectivity (R3) can be obtained as the difference
between the actual return and the sum of the other three components as:
R3 = Rp − (Rf + R1 + R2)
The return from pure selectivity is really the additional return obtained by a
portfolio manager for his superior stock selection ability. It is the return
earned over and above the return mandated by the total risk of the portfolio as
measured by standard deviation. Mathematically, this can be calculated as the
difference between the actual return on a portfolio and the return mandated
by its total risk. This is also known as Fama’s net selectivity measure. The
following formula may be used for calculating the measure.
Fama’s net selectivity = Rp − [Rf + (σp/σm) (Rm − Rf)]
where
Rp = Actual return on portfolio.
Rf = risk free rate.
Rm = return on market index.
σp = standard deviation of portfolio return.
σm = standard deviation of market index return.
We can illustrate Fama decomposition of portfolio return using the following
data on a portfolio.
Fama's decomposition may be stated as:
The return from net selectivity may be negative. This occurs when the actual
return realised on a portfolio is less than that mandated by the total risk of the
portfolio. This indicates that, due to poor stock selection, the portfolio has not
earned the return expected from it commensurate with its total risk.
The decomposition of total return is useful in identifying the different skills
involved in active portfolio management. A portfolio manager who attempts
to earn a higher return than the market return assumes higher risk and
depends on his superior stock selection ability to achieve the higher return. If
he is successful, the return due to pure selectivity would be positive.
Portfolio evaluation completes the cycle of activities comprising portfolio
management. It provides a mechanism for identifying weaknesses in the
investment process and for improving the deficient areas. Thus, portfolio
evaluation would serve as a feedback mechanism for improving the portfolio
management process.
SOLVED EXAMPLES
Example 1 An investor owns a portfolio that over the last five years has
produced 16.8 per cent annual return. During that time the portfolio produced
a 1.10 beta. Further, the risk free return and the market return averaged 7.4
per cent and 15.2 per cent per year respectively. How would you evaluate the
performance of the portfolio?
Solution The Treynor ratio can be used to evaluate the performance of the
portfolio in this case.
The ratio for the market index can be taken as the benchmark for evaluation.
The portfolio has a reward to volatility ratio higher than that of the market
index. Hence, the performance of the portfolio can be considered superior.
Example 2 You are given the following historical performance information
on the capital market and a mutual fund:
Year
Mutual fund beta
Mutual fund return
(per cent)
Return on market index
(per cent)
Return on
Govt. securities
(per cent)
1
0.90
−3.00
−8.50
6.50
2
0.95
1.50
4.00
6.50
3
0.95
18.00
14.00
6.00
4
1.00
22.00
18.50
6.00
5
1.00
10.00
5.70
5.75
6
0.90
7.00
1.20
5.75
7
0.80
18.00
16.00
6.00
8
0.75
24.00
18.00
5.50
9
0.75
15.00
10.00
5.50
10
0.70
−2.00
8.00
6.00
Calculate the following risk adjusted return measures for the mutual fund:
(a) Reward-to-variability ratio
(b) Reward-to-volatility ratio
Comment on the mutual fund’s performance.
Solution As the first step in calculation, the average values of the four
variables may be calculated.
Mutual fund performance:
For evaluating the mutual fund performance we have to calculate the Sharpe
and Treynor ratios for the market index to be used as the benchmark.
For calculating the Sharpe ratio for the market index, the standard deviation
of returns on the market index has to be calculated.
Calculation of Standard Deviation
2
Year
Return on market index (X)
X
1
−8.50
72.25
2
4.00
16.00
3
14.00
196.00
4
18.50
342.25
5
5.70
32.49
6
1.20
1.44
7
16.00
256.00
8
18.00
324.00
9
10.00
100.00
10
8.00
64.00
Total
86.90
1404.43
Example 3 Information regarding two mutual funds and a market index are
given below:
Assuming the risk-free return as 5 per cent, calculate the differential return
for the two funds.
Solution Differential return, as per Jensen ratio, is calculated as:
αp = Rp − E(Rp)
The expected return of the portfolio, E(Rp), can be calculated using the
CAPM formula.
E(Rp) = Rf + βp(Rm − Rf)
Gold fund: E(Rp) = 5 + 0.72 (10 − 5)
= 5 + 3.6 = 8.6 per cent
Platinum fund: E(Rp) = 5 + 1.33 (10 − 5)
= 5 + 6.65 = 11.65 per cent
Differential return
Gold fund: αp = 7 − 8.6 = − 1.6 per cent
Platinum fund: αp = 16 − 11.65 = 4.35 per cent
Example 4 From the information given in example 3, calculate net selectivity
measure for the platinum fund using Fama’s framework of performance
components.
Solution We have the following information:
Rp = 16 per cent
σp = 35 per cent
Rm = 10 per cent
σm = 24 per cent
Rf = 5 per cent
βp = 1.33
Fama’s decomposition may be stated as:
Rp = Rf + R1 + R2 + R3
Rf = 5 per cent
R1 = βp(Rm − Rf)
= 1.33(10 − 5) = 6.65 per cent
R2 = [(σp/σm) − βp](Rm − Rf)
= [(35/24) − 1.33](10− 5)
= (1.46 − 1.33) (5)
= 0.65 per cent
R3 = 16 − (5 + 6.65 + 0.65) = 16 − 12.3 = 3.70 per cent
Thus,
Rp = 5 + 6.65 + 0.65 + 3.70 = 16 per cent
Alternatively, Fama’s net selectivity can be directly calculated as follows:
Fama’s net selectivity
= Rp − [Rf + (σp/σm)(Rm − Rf)]
= 16 − [5 + (35/24) (10 − 5)]
= 16 − (5 + 7.3)
= 16 − 12.30 = 3.70 per cent
EXERCISES
1. Given the following information:
Portfolios
A
B
C
D
Beta
1.10
0.8
1.8
1.4
Return (per cent)
14.5
11.25
19.75
18.5
Standard deviation (per cent)
20.0
17.5
26.3
24.5
Risk free rate of return = 6 per cent
Market return = 12 per cent
Calculate
(a) Sharpe ratio
(b) Treynor ratio
(c) Jensen ratio
2. Given below are the historical performance information on the capital
market and a mutual fund.
Year
Mutual fund return
(per cent)
Mutual
fund beta
Return on market
index
Return on Govt.
securities
1
13.85
1.25
− 10.00
4.76
2
28.00
1.20
21.00
4.21
3
35.00
1.18
11.05
5.21
4
11.25
1.20
− 7.50
6.00
5
24.00
1.22
4.00
6.50
6
6.85
1.32
14.31
4.35
7
1.20
1.27
18.95
3.85
8
21.00
1.25
14.50
6.15
9
10.18
1.10
9.25
7.50
10
17.65
0.95
20.00
6.00
Calculate the following risk adjusted return measures for the mutual
fund:
(a) Sharpe ratio
(b) Treynor ratio
3. A mutual fund has earned an average annual return of 24 per cent over a
five year period while the average market return over the same period
was only 18 per cent. The risk free rate prevailing at the time was 7.5 per
cent. The mutual fund had a beta of 1.45. The standard deviation of
returns of the mutual fund and the market index were 40 per cent and 30
per cent respectively.
Calculate Fama’s net selectivity for the fund, showing the
decomposition of performance.
REVIEW QUESTIONS
1. Describe the different situations where evaluation of performance of
portfolios becomes necessary.
2. What are the different perspectives that can be adopted for evaluation of
performance of investment activity?
3. “Portfolio evaluation essentially comprises two functions, performance
measurement and performance evaluation.” Discuss.
4. What is meant by the holding period yield of a portfolio? How is it
calculated?
5. What are risk adjusted return measures? Give two examples.
6. Distinguish between Sharpe ratio and Treynor ratio.
7. What is differential return? Explain how Jensen ratio measures the
differential return of a portfolio.
8. Describe how the total return of a portfolio can be decomposed into
different sources, using Fama’s decomposition formula.
9. Explain Fama’s net selectivity measure.
19
FINANCIAL DERIVATIVES
In the financial market, individuals and organisations deal in financial assets
such as shares, bonds, foreign currency, loans, etc. The prices of these
financial assets often vary or fluctuate on a continuous basis. These
fluctuations create uncertainty in the financial market regarding the future
prices of these assets, and expose the dealers in the financial market to
considerable risk.
Let us consider a few examples. An investor may have purchased some
shares in the stock market, with the intention of selling them at a higher price
later. But there is considerable uncertainty regarding the future movement of
share prices in the stock market. Share prices may decline thereby exposing
the investor to the possibility of incurring a loss in his dealings. An investor
would want to avoid this risk and protect himself from the loss likely to arise
from such a risk.
An importer may have imported some goods from USA the payment for
which is due in three months’ time. He has to buy the necessary US dollars
from authorised foreign exchange dealers. Foreign currency exchange rates
fluctuate continuously in the currency market. As a result, there is the
possibility that the importer may have to pay more Indian rupees to buy the
US dollars after three months, if the dollar-rupee exchange rate declines
during this period. The importer is thus exposed to a risk and may incur a loss
on account of the uncertainty regarding the future movement of exchange
rates.
An exporter of goods faces a similar risk. He may have exported some goods
to Europe the payment for which is expected to be received after two months.
He will then have to convert the Euros that he receives into Indian rupees.
There is the possibility that the Euro-rupee exchange rate may rise during this
period and as a result the exporter may receive lesser Indian rupees while
converting the Euros. The continuous fluctuations in the exchange rates thus
expose the exporter of goods to considerable risk. Importers and exporters
would want to avoid the risk involved in their foreign currency deals. They
would desire to protect themselves from any loss in their foreign currency
transactions.
WHAT ARE FINANCIAL DERIVATIVES
Fluctuations in the prices of financial assets expose the dealers in such assets
to risk. The dealers would like to hedge the risk involved in their financial
transactions. Financial derivatives have evolved as instruments for hedging
the risk involved in buying, holding and selling various kinds of financial
assets. Basically, they are financial instruments for the management of risk
arising from the uncertainty prevailing in financial markets regarding asset
prices.
A financial derivative has an underlying asset, that is, a financial derivative is
evolved to hedge the risk involved in dealing in a particular financial asset
such as a share or a foreign currency. Hence, the value of a financial
derivative is derived from the underlying asset, and that is why it is known as
a derivative security.
Financial derivatives are designed to provide protection to participants in
financial markets against adverse movements in the prices of the underlying
assets. They facilitate the exchange of financial assets in future at prices
determined in the present.
Financial derivatives enable the participants to “lock in” a particular price for
the financial asset to be exchanged in the future. This effectively guards
against the uncertainties arising out of fluctuations in asset prices. For
example, an exporter who is expecting to receive the export proceedings in a
foreign currency sometime in the future, gets the facility to convert the
foreign currency into Indian rupees in future at a predetermined exchange
rate, by using a financial derivative. Thus, a market participant who faces the
risk of an adverse price movement in a financial asset, can use a financial
derivative as a means of reducing the risk by 'locking in' a suitable price for
the future dealings.
In general, a derivative security is one whose value is derived from the value
of the underlying asset. A financial derivative may be described as a financial
contract whose value is derived from the performance of financial assets,
interest rates, currency exchange rates or stock market indices. It may also be
defined as a contract that specifies the rights and obligations between the
issuer of the derivative security and the holder thereof to receive or deliver
future cash flows (or exchange of assets) based on some future event. Some
derivatives give the right to buy or sell the underlying asset at some point in
future for a predetermined price.
Financial transactions and investment activities often involve risk. Hence, it
has become necessary for those involved in investments and corporate
finance management to have a basic understanding of financial derivatives, as
these provide proper risk management tools. The derivative instruments are
now widely used and the volume of trading in these instruments is
substantial.
Financial derivatives include forwards, futures and options and the
underlying assets to which they relate include stocks, bonds, foreign
currencies and stock market indices. Standardised derivative contracts (e.g.
futures and options) are traded or transacted on organised exchanges and
these are known as exchange-traded derivatives. Other derivative contracts
that are privately negotiated between parties (e.g. forwards) are known as
Over-the-counter derivatives as they are not transacted on organised
exchanges but are privately traded. In these cases, the terms of the contract
are not standardised but can be customised to meet the needs of the
contracting parties. We shall now learn more about forwards, futures and
options.
FORWARDS
Forward contracts are a part of every day life. A person intending to buy a
new luxury car may have to enter into a forward contract for the same
because the luxury car may not be readily available for immediate delivery.
In such a situation, the customer books the car by making a deposit with the
car dealer. In effect, he is entering into a commitment to take delivery of the
car and make payment for it at a future date. This is the essence of a forward
contract. In this case the price and description of the car would be specified,
the delivery date might not be specified exactly.
“Forward contracts are commitments entered into by two parties to exchange
a specific amount of money for a particular good or service at a specified
future time.”1 More informally, a forward contract may be described as an
agreement to buy or sell an asset at a predetermined price and at a specified
future time. Thus, in a forward contract, the contract is initiated at one time
but the performance occurs at a subsequent time. The terms of the contract,
such as the price, delivery date and quantity and quality of asset are specified
at the time of initiating the contract, but actual payment and delivery of the
asset occur later. The asset involved may be a commodity such as wheat,
gold, etc. or a financial asset such as a foreign currency like US dollars.
One of the parties to a forward contract agrees to buy the underlying asset on
a certain specified future date for a certain specified price. The other party to
the contract agrees to sell the underlying asset on the same date for the same
price. The buyer is said to have a long position while the seller has a short
position. The price specified in the forward contract is referred to as the
delivery price and the time specified is referred to as the delivery date.
A forward contract is settled at maturity. That means the seller of the contract
delivers the specified asset to the buyer of the contract on the specified
delivery date in return for payment of the specified price. “A forward contract
is therefore a contract for forward delivery rather than a contract for
immediate or spot or cash delivery, and generally no money is exchanged
between the counterparties until delivery.”2
A forward contract is a simple derivative security. A derivative security is a
security whose value depends upon the value of another underlying asset. For
example, the price of a gold forward contract would depend upon the price of
gold in the cash market or spot market. The price of all forward contracts
would be linked to the price of the underlying assets.
Origin
Forward contracting has been in existence for many centuries. In fact, the
historical origins of forward contracts are obscure. “Some authors trace the
practice to Roman and even classical Greek times. Strong evidence suggests
that Roman emperors entered forward contracts to provide the masses with
their supply of Egyptian grain. Others have traced the origin of forward
contracting to India.”3
Nowadays forward contracts are so common that almost everyone has some
experience of such contracts.
Real Estate
Forward contracts are commonly used in real estate dealings. When the
contracting parties in a real estate deal come to an agreement as regards the
price of the property, they usually enter into a contract to buy and sell the
property at the agreed price within a specified time period. This is a typical
example of a forward contract.
In this case the forward contract is necessitated by a number of factors. The
buyer or seller would like to lock in the price agreed to by the counter parties.
The buyer might need some time to raise the required finance. The seller, on
the contrary, would like to ensure the fulfilment of the contract without undue
delay. A forward contract in real estate dealings is settled before the specified
maturity by execution of the sale deed by the seller and payment of cash by
the buyer. In real estate dealings, forward contracting is the normal practice
rather than being an exceptional or occasional practice.
Wheat
Now let us consider another example. A farmer who is cultivating wheat
would like to sell his wheat at the highest possible price when it is ready for
delivery. But at harvesting time the market would be flooded with wheat and
this oversupply is likely to dampen the price of wheat. The farmer may have
to sell off his wheat at a reduced price. Thus, the farmer faces a risk
(possibility of incurring a loss) due to fluctuations in the market price of
wheat. This risk can be avoided by entering into a forward contract for sale of
wheat at a reasonably high price. The forward deal can be struck while the
wheat is still growing. The delivery period would be so fixed as to coincide
with the harvesting time.
Let us assume that Rs.10 per kg would be a reasonable price for wheat. At
harvest time the price is likely to go down to Rs. 8 per kg, due to oversupply
of wheat in the market. If a farmer were to sell his wheat in the spot market at
harvest time, his price realisation would be Rs. 2 per kg short of the price
available earlier. In order to eliminate this loss and to guarantee the best price
available in the market, a farmer can enter into a forward contract for sale of
wheat at Rs. 10 per kg for delivery in the harvesting month. If he makes such
a deal the counter party to the deal would be obliged to buy wheat from the
farmer at Rs. 10 per kg at the time of harvest when wheat is ready for
delivery. Through a forward contract the farmer thus guarantees a reasonably
good price for his wheat and thereby eliminates the risk due to fluctuations in
the market price of wheat.
A doubt that naturally arises is who would possibly be the counter party to
such a deal which seems to favour the farmer. A wheat processing company,
such as a bread manufacturer or flour mill, would require large quantities of
wheat throughout the year as raw material for their manufacturing activities.
Due to the fluctuations in the market price of wheat, these companies may be
forced to buy wheat at high prices during some months of the year if they
operate in the spot market. This will lead to an increase in the cost of
production and a reduction in the profit margin. In other words, these
companies too face a risk (possibility of reduction in their profit) due to
fluctuations in the market price of wheat. They face uncertainty regarding the
future price of wheat. Hence, they would like to get a steady supply of wheat
at a reasonable and certain price throughout the year. This objective can be
achieved by entering into a forward contract to buy wheat at a predetermined
price which would be reasonable to the wheat processor. By entering into
different forward deals maturing at different time periods, a regular supply of
wheat at a reasonable and certain price can be ensured. Thus, processing
companies can fit well into the role of a counter party to the wheat farmer
who desires to sell wheat in the forward market.
The other group of persons who would like to act as the counter party to the
wheat farmer are the speculators. They engage in two-way trade (buy and
sell) in order to make profit from the movements of prices of any assets. They
would be prepared to act as counter party either to the wheat farmer or to the
wheat processing company in order to gain from the movements in the
market price of wheat. They operate both in the spot market as well as in the
forward market.
Gold
Gold is another commodity whose price fluctuates almost daily. Even though
the daily fluctuations may be marginal, the price fluctuations can be
substantial between different months of the year. Much gold is purchased by
jewellers for conversion into jewellery. The Government may also buy and
sell gold in order to adjust its gold reserves. Forward contracts can be used to
hedge the risk involved in gold trade.
Let us take the case of a jeweller who would like to buy gold at a low price in
order to convert it into valuable pieces of jewellery. Higher price of gold
would mean lower profit for the jeweller. Because of the wide fluctuations in
the market price of gold between different months of the year, the jeweller
may have to buy gold at high prices frequently if he operates solely in the
spot market. By entering into forward deals to buy gold at a reasonable price
he can isolate himself from the price fluctuation in the market. Forward
contracts enable a jeweller to be certain about the price he has to pay for the
gold he is to take delivery in the future. These contracts remove the
uncertainty resulting from price fluctuations of gold.
Suppose that the price of gold in the spot market is currently Rs. 400 per
gram. If a jeweller feels that a price range of Rs. 400 to Rs. 410 per gram is
reasonable, he can lock in this price for his future purchases by entering into
forward contracts at a delivery price not exceeding Rs. 410 per gram. If he
succeeds in doing that, the uncertainty associated with the future price
movements of gold will not affect him in the least, because he has already
hedged the risk effectively.
Foreign Currency
Each country has its own currency, such as the rupee in India, the dollar in
USA, the pound sterling in UK, the euro in Europe, the yen in Japan, the
franc in Switzerland, the kroner in Sweden, the dinar in Kuwait, the riyal in
Saudi Arabia, etc. Foreign currency means all currencies other than the home
currency. As far as India is concerned, all currencies other than the Indian
rupee are foreign currencies.
With increase in globalisation, financial transactions between nations have
increased manifold. Individuals and corporates of one country may trade with
individuals and corporates of other countries, may provide services to other
countries or receive services from other countries, may invest money in other
countries or accept investment of money from other countries. All these
transactions result in exchange of currencies between nations. Hence, foreign
currencies are often referred to as foreign exchange.
Global transactions thus necessitate exchange of one currency for another.
The rate of such exchange between currencies is known as the exchange
rate. A foreign exchange rate is the price of one currency in terms of another
currency. For example, one US dollar may be exchanged for ` 43.41; one
pound sterling may be exchanged for ` 81.45, one pound sterling may be
exchanged for US dollars 1.8763, etc. The exchange rates between currencies
depend upon a host of factors and keep changing on a continuous basis. Such
fluctuations in exchange rates is a source of risk for dealers in foreign
currency.
Let us consider the case of an importer who has imported goods worth US
*dollar*1,00,000 from U.S.A. He is required to make the payment in US
dollars after three months. If the current exchange rate is *dollar*1 = ` 43.41,
he would require ` 43,41,000 to buy *dollar*1,00,000. As the dollars are not
required immediately he is likely to buy them only after three months when
the payment is due. The amount of rupees required to buy *dollar*1,00,000
would depend upon the exchange rate prevailing at that time. Suppose the
exchange rate changes to *dollar*1 = ` 44.10, the importer would require `
44,10,000 to purchase *dollar*1,00,000. The importer thus suffers a loss of `
69,000 (` 44,10,000 − ` 43,41,000) on account of the fluctuation in exchange
rates.
The uncertainty of future exchange rates is a source of risk for those dealing
in foreign currency. However, this risk due to exchange rate fluctuations can
be effectively hedged by entering into forward contracts to buy or sell the
foreign currency. In the case of the importer considered above, he can hedge
the risk and eliminate any possible loss due to an adverse movement in the
exchange rate by entering into a forward contract to buy US dollars at a
delivery price (forward exchange rate) close to the current exchange rate of `
43.41 for delivery three months hence. The counter party, then, would be
obliged to sell US dollars to the importer at the agreed exchange rate,
whatever be the exchange rate prevailing in the foreign exchange market at
that time.
Forward contracts are very extensively used in foreign currency dealings to
hedge the risk arising from exchange rate fluctuations. Resident individuals
and companies may have to buy foreign currencies for making payments
abroad. They may also have to convert foreign currencies they receive from
other countries to Indian rupees for use within the country. All of them face
financial risk due to exchange rate fluctuations. Forward deals in foreign
currencies are common among foreign exchange users and dealers.
HEDGING OF FOREIGN EXCHANGE RISK THROUGH
CURRENCY FORWARDS
An importer or exporter can face considerable foreign exchange risk due to
exchange rate fluctuations when their trade is invoiced in a foreign currency.
An importer is generally not required to make the payment immediately. He
gets some credit period. However, his account payable is exposed to foreign
exchange risk because the payment has to be made in a foreign currency. The
amount of rupees required to meet his payment would depend upon the spot
exchange rate prevailing at the due date for making the payment. This
exposure can be hedged through a currency forward deal.
Suppose that an Indian company has imported some goods worth
*dollar*1,00,000 from U.S.A. and that the payment is due in three months’
time. There is uncertainty about the amount of rupees that would be required
to buy *dollar*1,00,000 at the due date because of exchange rate fluctuations.
The company can hedge this risk by buying one lakh US dollars forward for
delivery on the due date of payment of the import bill. Let us suppose that the
company concludes such a forward deal at a forward rate of ` 43.85 per US
dollar. By entering into such a forward deal the company eliminates the
uncertainty regarding the rupee cost of his imports. Whatever be the actual
spot rate at the time of settlement, the importing company can buy the dollars
at ` 43.85.
An exporter faces a similar foreign exchange risk on his account receivable
when the trade is invoiced in a foreign currency. The amount due on account
of the export trade is likely to be received only after a delay of a few months.
The amount of rupees that he will realise by converting the foreign currency
into Indian rupees when it is received would depend upon the spot rate at that
time. The exporter can hedge this risk by selling forward the foreign currency
expected to be received later. He can thus eliminate the possibility of loss on
conversion of the foreign currency.
Such a currency forward deal is outlined below:
Currency Forward Deal
Export contract data
Exporter
:
Indian company
Importer
:
American company
Currency of invoice
:
US Dollar
Invoice value
:
*dollar*2,00,000
Invoice date
:
1 July
Credit period
:
3 months
Due date of Receipt
:
1 October
Exchange Rate Quotes on 1 July (Rs./US Dollar)
Spot
43.30
43.73
July
43.47
43.91
Aug.
43.62
44.06
Sept.
43.74
44.19
Oct.
43.87
44.32
Forward
Forward Deal Transactions
1 July Indian exporting company sells *dollar*2,00,000 three months forward
at ` 43.87 per US dollar.
1 October Indian exporting company receives *dollar*2,00,000 from the
American company.
1 October Indian company delivers *dollar*2,00,000 to the foreign exchange
dealer and receives ` 87,74,000 at the rate of ` 43.87 per US dollar.
ADVANTAGES OF FORWARD CONTRACTS
“A forward contract is an agreement between two counter parties that fixes
the terms of an exchange that will take place between them at some future
date. The contract specifies: what is being exchanged ..., the price at which
the exchange takes place, and the date (or range of dates) in the future at
which the exchange takes place.”4 Forward contracts are used in market
environments where the price of the underlying asset fluctuates considerably.
The price fluctuation gives rise to uncertainty regarding the future movement
of prices. This uncertainty exposes the trading parties to considerable risk. By
locking in a fixed price today of an exchange that is to take place at some
future date, forward contracts help to eliminate the risk. Thus, forward
contracts are an ideal tool for hedging the risk arising from price fluctuations
of underlying assets.
In forward contracts, the terms of the exchange are determined by mutual
agreement to suit the convenience of the two counter parties. Futures
contracts, which provide an alternative method of hedging risk due to price
fluctuations of underlying assets, are standardised agreements to exchange
specific types of assets, in specific amounts and at specific future delivery
dates. The details of the contract are not negotiable between the counter
parties in a futures contract. The advantage of a forward contract over a
futures contract is that it can be tailor-made to meet the requirements of the
two counter parties to the contract, in terms of the size of the contract as well
as the date of forward delivery.
DISADVANTAGES OF FORWARDS
Forward contracts have two major disadvantages. Forwards involve credit
risk or default risk. There is a possibility that one of the counter parties to
the contract may default and fail to fulfil his obligation under the contract.
Even though the forward price of an asset is an estimate of the expected spot
price at the time of forward delivery, unexpected changes do occur in the
future movements of spot prices. As a result, the realised or actual spot price
at the time of delivery of the asset may differ from the forward price agreed
to by the counter parties.
If the actual spot price is higher than the forward price, the counter party
taking delivery of the asset (buyer) is in an advantageous position because he
gets the asset at a cheaper price than the prevailing market price. The other
party (seller) is in a disadvantageous position because he has to deliver the
asset at a price which is lower than the prevailing market price. If the spot
price is lower than the forward price, the buyer would be at a disadvantage
and the seller would benefit. The party in the disadvantageous position would
naturally be tempted to default. The wider the gap between the spot price
prevailing at the time of delivery and the forward price agreed to earlier, the
greater the incentive to default. In the forward contract, being a private
agreement between two parties, there is no mechanism to prevent default by
either party. This is known as default risk or credit risk.
Let us consider an Indian importer who has contracted to purchase
*dollar*1,00,000 three months forward at ` 43.75 per US dollar. If, at the
settlement date, the spot exchange rate is ` 44.00 per US dollar, the importer
is in an advantageous position because he gets the dollars at ` 43.75 when the
rate in the spot market is higher at ` 44.00. The foreign exchange dealer who
is obliged to sell the dollar at a lower price to the importer may default. If, on
the contrary, the spot exchange rate at settlement date happens to be ` 43.55,
the importer has an incentive to default because he can purchase the dollars in
the spot market at a cheaper rate at ` 43.55 than from the foreign exchange
dealer as per the forward contract at ` 43.75.
The second disadvantage of forward contracts is illiquidity. A forward
contract cannot be cancelled except with the consent of both the counter
parties. Neither can the obligations of a counter party under the contract be
transferred to a third party. Thus, a forward contract has no liquidity and no
marketability. It is normally settled at maturity through fulfilment of mutual
obligations by the counter parties. The illiquidity of forwards arises from its
characteristic of being a private agreement between two parties.
Although forwards are useful in hedging the risk exposure of parties trading
the underlying asset, their inherent disadvantages limit the scope of their use
in many markets. However, in foreign exchange markets around the globe,
forwards are extensively used to cover foreign exchange risk exposure.
REVIEW QUESTIONS
1. What are financial derivatives?
2. How do financial derivatives help to hedge the risk in financial
transactions?
3. What is meant by over-the-counter derivative?
4. “Forward contracts are a part of everyday life.” Explain.
5. Define a forward contract.
6. Explain the meaning of a forward contract.
7. Give examples of forward contracts in commodities.
8. Explain how currency forwards can be used to hedge the risk in foreign
exchange deals.
9. Discuss the advantages of forward contracts.
10. What is credit risk associated with a forward contract?
11. Discuss the disadvantages of forward contracts.
REFERENCES
1. Elton, Edwin J., and Martin J. Gruber, 1994, Modern Portfolio Theory
and Investment Analysis, 4th ed., p. 167, John Wiley & Sons, Singapore.
2. Blake, David, 1992, Financial Market Analysis, p. 158, McGraw-Hill,
London.
3. Kolb, Robert W., 1997, Understanding Futures Markets, 3rd ed., pp.
2−3, Prentice-Hall of India, New Delhi.
4. Blake, op.cit., p.158.
20
FUTURES
Futures contracts, better known as futures, constitute an important
instrument for managing or hedging the risk in commodity and financial
markets due to price fluctuations in the markets. The essential nature of a
futures contract is the same as that of a forward contract. Both involve a
contract to exchange some assets, initiated at one time, to be performed at a
subsequent time. However, the features and modalities of operation of the
two are so vastly different that forwards and futures have become two
different types of instruments used for risk management. In fact, futures
contracts have been designed to remove the disadvantages of forward
contracts.
FUTURES CONTRACTS
“A futures contract, like a forward contract, is an agreement between two
parties to buy or sell an asset at a certain time in the future for a certain
price.”1 While the details of a forward contract are negotiated between the
parties to the contract, futures contracts are normally traded on an organised
or regulated exchange where traders used to assemble periodically on the
floor of the exchange to buy and sell futures contracts generally by open
outcry. The futures exchanges are now shifting to online trading using a
networked computer system which facilitates screen-based trading. To make
such trading possible, the exchange specifies certain standardised features for
the contracts. Hence, “futures contracts are standardised agreements to
exchange specific types of goods, in specific amounts and at specific future
delivery or maturity dates”.2
A wide variety of commodities and financial assets form the underlying
assets in futures contracts. Wheat, sugar, wool, gold, aluminium, copper, etc.
are some of the commodities underlying futures contracts. Stocks, stock
indices, foreign currencies, bonds, etc. are the financial assets underlying
futures contracts.
Futures contracts can be broadly grouped into two types: commodity futures
and financial futures. In a commodity future, the underlying asset would be
a commodity such as wheat, cotton, pepper, etc. A futures contract on
financial assets such as foreign currencies, stocks, bonds, etc. is known as a
financial future.
An exchange initiates a futures contract by listing it for trading. The
exchange specifies the terms of the contract, such as the underlying asset, its
quality, the contract size (quantity of asset to be delivered per contract), the
delivery place and time.
The Asset
The underlying asset may be a commodity or a financial asset. When
specifying the asset underlying a futures contract, the exchange specifies the
grade or grades of the asset that are acceptable. The contract size refers to the
quantity or amount of the asset that has to be delivered under the contract.
For example, one gold futures contract may consist of 100 gms of gold. One
wheat futures contract may consist of 5000 bushels. The contract size should
be suitable for trading; it should be neither too large nor too small.
Delivery Terms
The place where delivery of the asset is to be made by the seller is specified
by the exchange. An exact delivery data is not specified for a futures contract;
rather, a futures contract is referred to by its delivery month such as March
gold future. The exchange specifies the precise period during the month when
delivery has to be made by the seller. For commodity futures, the delivery
period is often the whole month. The seller then can choose the exact time
during the delivery month when he will deliver the asset. For example, a
December wheat future may be delivered on any day in December, before the
expiry day.
The exchange specifies when trading in a particular delivery month’s contract
may commence. At any given time, contracts of different delivery months
may be trading in an exchange.
Price and Price Limits
Futures contracts of the same underlying asset with different delivery months
are essentially different contracts. The price of a futures contract is
determined on the floor of the exchange by the forces of demand and supply.
If there are more buyers for a particular contract, the price of the contract
goes up, and vice versa.
For most futures contracts, limits are specified by the exchange for daily
price movements. These daily price movement limits are put in place so as to
prevent large fluctuations in price movements within a trading day. If, on a
particular day, the price of the future moves down by the specified limit
amount, the futures contract is said to be limit down and normally trading on
the contract ceases for that day. When the price moves up by the specified
limit amount, the futures contract is said to be limit up with no further trading
on the contract for the day.
Long and Short Positions and Open Interest
There are two parties to every futures contract: a buyer and a seller. The act
of buying a futures contract is characterised as going long on the contract.
The act of selling a futures contract is similarly characterised as going short
on the contract. The buyer is said to have a long position and the seller is
said to have a short position. When a futures contract is first listed for
trading by an exchange, interested parties take long or short positions on the
contract. When one trader takes a long position on the contract for a
particular price and another trader takes a short position on the contract at the
same price, it generates a trading volume of one contract. At this point there
is one contract which remains to be performed or settled through delivery of
the asset in the future. Thus, there is one open contract. This is also referred
to as open interest, which is the terminology used to describe the number of
open contracts or contracts remaining to be settled in future on any particular
day.
A trader may take a long position on more than one contract of the same
delivery month. For example, a trader who buys five September wheat
futures has five long positions and gives rise to five open interests. The
trading volume of a particular trading day represents the number of new
contracts entered into by traders on that day in a specific futures contract such
as November gold futures. The open interest in a specific futures contract
represents the cumulative total of all contracts remaining to be settled from
the commencement of trading in that contract till date. This keeps on
increasing as new contracts are entered into and declines when outstanding
contracts are settled or closed out.
FEATURES OF FUTURES CONTRACTS
A futures contract has several distinguishing features which make it a suitable
instrument for hedging risk.
Organised Exchange
Futures contracts are always traded on organised futures exchanges. A futures
exchange is a voluntary, non-profit association of certain members. It is an
organisation or institution created to facilitate trading in futures contracts. Its
functioning is governed by a set of rules and procedures.
Virtually all of the futures exchanges in the United States date from the late
19th or early 20th century. They all started as commodity exchanges, but
since the early 1980s trade in financial futures has become more and more
important for most of them. Europe has some of the world’s oldest as well as
some of the world’s newest commodity exchanges. Other countries of the
world have also started commodity exchanges and set up separate markets for
derivatives trading.
Across the globe we find different models of futures trading. There are some
futures exchanges which have trading in commodity futures as well as
financial futures. There are other futures exchanges which are commodity
futures exchanges allowing trading in commodity futures only. Financial
futures are sometimes traded along with stocks in the stock exchanges,
having a separate segment for trading in futures and options. There are also
instances of financial futures being traded in separate futures and options
exchanges.
Commodity futures markets have a long history in India. The first organised
futures market for various types of cotton appeared in 1921. In the 1940s,
trading in forward and futures contracts as well as options was either
outlawed or made impossible through price controls. This situation continued
until 1952, when the Government of India passed the Forward Contracts
Regulation Act. Again, during the 1960s, the Government either banned or
suspended futures trading in several commodities. The government policy,
however, softened in the late 1970s. The ongoing process of economic
liberalisation and globalisation has brought about a reconsideration of the
role of futures market. Futures trading in a wide range of commodities has
been revived.
In India, now there are three national commodity futures exchanges, namely
1. National Multi-Commodity Exchange of India Ltd. (NMCE), Ahmedabad
2. Multi-Commodity Exchange of India Ltd. (MCX), Mumbai
3. National Commodity and Derivatives Exchange Ltd. (NCDEX), Mumbai.
These exchanges provide facilities for nationwide trading of commodity
futures contracts in several commodities. In addition to these, there are other
commodity exchanges located in various parts of the country, specialising in
the trading of specific commodity futures such as the International Pepper
Futures Exchange set up in Kochi, and the Coffee Futures Exchange of India
with headquarters at Bangalore. In India, futures trading is carried on in most
of the major commodities such as cotton, coffee, wheat, raw jute, sugar,
rubber, spices such as pepper, cardamom, turmeric, metals such as
aluminium, copper, gold, lead, tin, zinc, silver, various kinds of edible oils,
oil seeds and oil cakes.
The Forward Markets Commission (FMC), set up under the Forward
Contracts (Regulation) Act of 1952, is the regulatory body for commodity
futures trade in India.
The trading of financial futures contracts is of recent origin in India. It was in
the year 2000 that trading in financial futures commenced in India at BSE
and NSE. Both the stock exchanges have separate futures and options
segment for trading in financial derivatives. Their trading system provides a
fully automated screen-based trading for derivatives on a nationwide basis.
The system supports an anonymous order-driven market. The derivatives
trading terminals of both the exchanges are available all over the country.
Trading in financial derivatives is regulated by SEBI.
Standardised Terms
In a forward contract, the terms of the contract such as quality, quantity,
delivery date and delivery price are negotiated between the contracting
parties and finalised as per their mutual needs and conveniences. This is
possible because a forward contract is a private bilateral agreement traded
over the counter and to be settled in future between the contracting parties. A
futures contract is a derivative security to be traded in an organised exchange.
As such the terms of the contract need to be standardised to facilitate such
trading. The exchange specifies the terms of the contract such as: quantity
and type of asset to be delivered, the delivery date, and the place of delivery
and the process of delivery. The contracting parties have to abide by the
standardised terms specified by the exchange.
Clearing House
Each futures exchange has a clearing house. It is the clearing house which
arranges for the delivery of the asset and the payment of money to the
counter parties. This is done by the clearing house itself becoming the
counter party to the original parties of the contract. The original parties of the
derivative security (futures contract) are the buyer and the seller of the futures
contract. The seller of a gold futures contract has to deliver the gold on the
future delivery date and receive payment from the buyer of the futures
contract. The buyer has to make payment on the future date and take delivery
of the gold. Here, the clearing house becomes the counter party to the buyer
to deliver the asset. The buyer has to make payment to the clearing house.
Similarly, the clearing house becomes the counter party to the seller to make
payment for the asset and the seller has to deliver the asset to the clearing
house. The clearing house thus guarantees fulfilment of all futures contracts
by intervening in all transactions and becoming the formal counter party to
every transaction.
Margin System
When the clearing house becomes the counter party in each futures
transaction, the obligations of the original parties have to be fulfilled towards
the clearing house. The seller has to deliver the asset to the clearing house
and the buyer has to make the payment to the clearing house. If the original
parties default in fulfilling their obligations to the clearing house, the loss has
to be borne by the clearing house. In order to avoid or eliminate such a risk,
the clearing house has prescribed a margin system for trading in futures
contracts.
A margin is a deposit to be made to the clearing house by the parties entering
into a futures contract. There are three types of margins, namely initial
margin, maintenance margin and variation margin. At the time of execution
of a futures contract, both the buyer and the seller are required to deposit the
initial margin. This initial margin is sometimes referred to as performance
margin. The amount of initial margin is fixed as a percentage of the base
value of the futures contract, ranging from 5 per cent to 25 per cent. The
margin percentage may vary from contract to contract based on the risk
involved in the underlying asset.
The futures contract is revalued daily on the basis of the market price
prevailing each day. The change in the value of the contract is daily adjusted
in the margin accounts of the parties. When the market price of the
underlying asset declines, the buyer of the contract suffers a loss to the extent
of change and the seller of the contract gains; the decline in the value of the
futures contract is debited to the margin account of the buyer and credited to
the margin account of the seller. On the contrary, when the price of the
underlying asset increases, the buyer gains and the seller is set to suffer a
loss. The increase in the value of the contract is credited to the buyer’s
margin account and debited to the seller’s margin account. This process is
known as marking-to-market and it effectively keeps the margin amount in
line with the current market conditions.
As the futures contract is marked-to-market on a daily basis, the balance in
the margin account of the buyer and the seller keeps changing. However, the
buyer and the seller are expected to maintain a minimum balance, known as
maintenance margin, in their margin accounts throughout the duration of
the contract. The maintenance margin may be fixed as a certain percentage,
for example 75 per cent, of the initial margin. If the balance in the margin
account drops below the maintenance margin level, a margin call is issued
by the exchange to the party concerned. Additional funds have to be
deposited into the margin account by the party immediately so as to bring the
balance in the margin account to the level of the initial margin. The additional
funds to be deposited on the basis of the margin call are known as variation
margin. If the additional funds (variation margin) are not deposited within
the stipulated time, the exchange cancels the contract and recovers the loss, if
any, from the defaulting party. The margin system ensures that the
contracting parties will not default in fulfilling their obligations to the
clearing house as the counter party.
In order to understand the marking-to-market process and its impact on the
margin balances of the trading parties, let us consider an example.
Futures Contract Data
Gold futures contract: size = 100 gms
Investor buys one December gold futures contract on 1 November at ` 400/per
gram
Value of contract: ` 400 × 100 gm = ` 40,000
Initial margin: 10 per cent = ` 4000
Maintenance margin: 75 per cent of initial margin = ` 3000
The daily marking-to-market can be illustrated in a tabular form.
Marking-to-Market: Buyer’s Margin Account
Day
Closing price of
Daily
Cumulative
Margin
Variation
gold/gm
gain (loss)
gain (loss)
balance
margin
Nov. 1
400
—
—
4000
Nov. 2
403
300
300
4300
Nov. 3
398
(500)
(200)
3800
Nov. 4
390
(800)
(1000)
3000
Nov. 5
392
200
(800)
3200
Nov. 6
387
(500)
(1300)
2700
Nov. 7
394
700
(600)
4700
Nov. 8
401
700
100
5400
Nov. 9
405
400
500
5800
Nov. 10
410
500
1000
6300
1300
On November 2, there is a gain of ` 300 to the buyer on account of increase
in the price of gold. This amount is credited to the margin account and the
balance becomes ` 4300. On the next day there is a loss of ` 500 on account
of decline in price of gold and this loss is debited to margin account. On
November 4, the margin balance becomes just equal to the maintenance
margin of ` 3000. However, on November 6, the margin balance drops below
the maintenance margin and gives rise to a variation margin of ` 1300 which
has to be deposited into the margin account immediately. On November 10,
the margin balance is ` 6300 which represents a profit of ` 1000 (` 6300 − `
5300 deposited as initial and variation margin) as the price of good is higher
by ` 10 compared to the buying price.
The seller’s margin account will show a reverse position as shown below.
Marking-to-Market: Seller’s Margin Account
Day
Closing price of gold/gm
Daily
Cumulative
Margin
Variation
gain (loss)
gain (loss)
Balance
margin
Nov. 1
400
—
—
4000
Nov. 2
403
(300)
(300)
3700
Nov. 3
398
500
200
4200
Nov. 4
390
800
1000
5000
Nov. 5
392
(200)
800
4800
Nov. 6
387
500
1300
5300
Nov. 7
394
(700)
600
4600
Nov. 8
401
(700)
(100)
3900
Nov. 9
405
(400)
(500)
3500
Nov. 10
410
(500)
(1000)
3000
On November 10, the margin balance in the seller’s margin account is ` 3000,
representing a loss of ` 1000 which is the gain to the buyer on that day.
In the marking-to-market process, as the price of the underlying asset
changes, the value of the futures contract also changes; the resulting change
is credited to the party who gains and debited to the party who loses. The
margin accounts of the parties are thus adjusted with the gain/loss in the
transaction.
Closing of Futures
A forward is a contract to deliver an underlying asset on a future date at a
price already agreed upon. A forward contract is settled on the delivery date
by delivery of the asset by the seller and payment of money by the buyer. A
futures contract is also a contract to deliver an underlying asset on a future
date at a price already agreed upon. But it is a contract with standardised
terms traded on an organised exchange with the clearing house of the
exchange acting as counter party to the transaction to guarantee fulfilment of
the contract. A futures contract can be settled in two ways. The first method
is through the exchange of the asset and the cash on the delivery date. The
second method is known as cash settlement which is effected by entering
into a reverse trade on any day before the delivery date. For example, a
person who has bought a gold futures contract may hold his long position till
the delivery date and take delivery of the gold and make payment for it. Or
else, he may enter into a reverse trade, that is, sell a gold futures contract on
any day before the delivery date. His open position would be closed and he
would receive the difference between the selling price and the buying price
when the selling price is higher. If the selling price is lower than his buying
price, he would suffer a loss and make the payment to the exchange.
Since there is a system of daily marking-to-market, the margin balance of the
parties would reflect their gain or loss each day. When a reverse trade is
entered into for cash settlement, the margin account of the party would be
closed and the balance in his margin account would be refunded to him. In
the seller’s margin account table shown on the previous page, if the seller
opts for cash settlement on November 10, through a reverse trade to buy gold
future entered into with any other party, his short position will be closed and
the balance in his margin account (` 3000) would be refunded. He had
deposited ` 4000 as initial margin and hence suffers a loss of ` 1000. This is
because his selling price on November 1 was ` 400, whereas his buying price
on November 10 was ` 410, resulting in a loss of ` 10 per gram of gold.
The buyer of the original contract, whose margin account is shown in the
respective table, may continue to hold an open position. He may either
continue till the delivery date and take delivery of the gold or he may opt for
cash settlement on any day before the delivery date. If he opts for cash
settlement on November 8, he would receive ` 5400 from the clearing house
being refund of the margin balance on that day. It would represent a profit of
` 100 (` 5,400 − ` 5,300 deposited as initial margin and variation margin), the
selling price (` 401) being higher than the buying price (` 400) by one rupee.
In the futures market two types of operators are to be found: hedgers and
speculators. Hedgers may be end-users who need the underlying asset and
use the futures contract to hedge the risk arising from the price fluctuations of
the underlying asset. Hedgers may also be investors who have or hold the
underlying asset and would like to hedge the risk from adverse movements in
the prices of the underlying asset. Speculators are traders who do not have or
who do not need the underlying asset; they anticipate price movements of the
underlying asset which will provide an opportunity for making profit. They,
therefore, take long or short positions in order to close these positions later
and book the profit. But losses are equally possible if the price movements
are against their anticipations.
The two major disadvantages of a forward contract are illiquidity and default
risk or credit risk. The futures contract has overcome these two limitations.
The default risk, or possibility of default by any of the parties, is removed
with the introduction of the margin system and also the clearing house acting
as the counter party in each transaction. Trading in organised exchanges with
the facility for cash settlement provides liquidity to futures contracts, as a
secondary market is created for futures contracts.
Futures contracts are generally available on:
1. Agricultural commodities such as wheat, cotton, coffee, etc.
2. Precious metals and minerals such as gold, silver, petroleum, etc.
3. Foreign currency such as dollar, euro, etc.
4. Stock market indices
5. Stocks.
We shall now learn about futures on stock market indices. These are peculiar
in the sense that the underlying asset is not a tangible asset or real asset that
can be physically delivered but a concept or a mathematical calculation.
INDEX FUTURES
A stock index is an indicator of the general level of stock prices. It is
calculated by taking into consideration the prices of a representative group of
stocks traded in the stock market. Such a stock market index can be used as
an underlying asset to create a futures contract known as Index Futures.
Futures contracts are available on many stock indices across the globe. Some
of the stock indices on which futures are traded include S and P 100, S and P
500 in USA, Nikkei 225 in Japan, FTSE 100 in UK, DAX in Germany, CAC
40 in France, and Nifty in India. The value of a particular stock index futures
contract depends upon the sum of money allotted per index point. The sum of
money allotted per index point for the FTSE 100 stock index is £25. Hence, if
the FTSE 100 stands at 2100 points, the value of a futures contract on FTSE
100 at that point would be £52,500. The sum of money allotted per index
point in the case of Nifty is ` 1. When Nifty stands at 1990, the value of a
futures contract on Nifty would be ` 1990.
It may be noted that it is not possible to settle an index futures contract on the
delivery date by physical delivery of the index. Only a cash settlement is
possible in the case of stock index futures. The outstanding contracts can be
closed by payment or receipt of cash, representing the difference between the
contract price and the settlement price. If the settlement price is higher than
the purchase price of an index future, the buyer of the contract would receive
the difference. On the contrary, if the settlement price is lower than the
purchase price of an index future, the buyer would pay the difference to the
counter party (the clearing house). Similarly, the seller of an index future
would receive payment when the settlement price, is lower than his selling
price, and he will make payment when the settlement price is higher than his
selling price.
Investors may use index futures for hedging their risk, while speculators may
use them for making gains from the movement of the underlying stock
indices.
Hedging
An investor who holds a portfolio of securities may be anxious about the
possibility that the prices of his shares might fall. He thus faces a risk of
reduction in the value of his portfolio on account of an adverse movement of
share prices in the stock market. He can effectively hedge this risk by taking
a position in the stock index futures that will provide him a gain in the event
of a fall in share prices. If the investor anticipates a fall in share prices, he
should take a short position (or sell) in the required number of stock index
futures. He would thus be guaranteeing a selling price for sale of the stock
index for a specific period in the future. If there is a fall in share prices in the
future as anticipated, the stock index would also fall correspondingly. The
investor can then close out his position in the index futures by taking a long
position (or buying) in the same number of contracts. The buying price would
be lower than his predetermined selling price. The excess of the selling price
over the buying price would be received by the investor, representing his gain
in the futures transaction. The reduction in the value of his portfolio would be
compensated by the gain in the index futures transaction without making any
change in his original portfolio of shares. If, against his expectations, the
share prices were to rise, the investor would suffer a loss in his futures
transaction but the value of his portfolio of shares would rise proportionately
to compensate the loss.
Let us consider an investor who holds a portfolio of shares valued at ` 60,000.
He anticipates a fall in equity prices and would like to avoid a reduction in
the value of his portfolio. The NSE index Nifty on which futures contracts
are available now stands at 2000.
In order to hedge the risk in this case, the investor needs to sell Nifty futures
contracts. As the monetary value assigned to Nifty futures is ` 1 per index
point, the value of one Nifty future at the current index value would be `
2000. As the value of the investor’s portfolio is ` 60,000, he needs to sell 30
Nifty futures to hedge his portfolio. Let us assume that the investor sells 30
Nifty futures at ` 2000 per contract. If there is a fall in equity prices in the
stock market as anticipated, there would be a reduction in the value of the
investor’s portfolio and also a fall in the value of the stock market index. Let
us assume that there has been a general decline in share prices to the extent of
10 per cent over a period of one month. This means that the value of the
investor’s portfolio would have declined by ` 6000 and the stock index would
be at 1800 by the month end.
The investor can now close out his position in the index futures by buying 30
Nifty futures at the current price of ` 1800. The selling price being higher
than the buying price by ` 200, the investor would receive ` 6000 (` 200 × 30
contracts) on buying 30 Nifty futures. The gain of ` 6000 from the index
futures trading would thus compensate the reduction in the value of his
portfolio. Thus trading in the index futures has helped the investor to hedge
his risk.
A long position in index futures can also be used as a hedging tool. An
example would illustrate this strategy. Let us consider a mutual fund
company which has announced an investment scheme and is expecting to
receive ` 50,00,000 within a month for investment in the stock market. The
research wing of the company has estimated that the prices of equity shares in
the market would rise in the meantime. The mutual fund thus faces a risk of
having to buy the shares from the market at higher prices. By taking a long
position (or buying) in index futures, the mutual fund can hedge this risk.
Let us assume that Nifty currently stands at 2000. The fund needs 2500 Nifty
futures to cover its expected receipt of ` 50,00,000. The mutual fund can buy
2500 Nifty futures at ` 2000 per contract. If, by the end of the month, Nifty
rises to 2200 on account of a general increase of 10 per cent in equity prices,
the fund can now close out its long position in Nifty futures by selling 2500
Nifty futures at the current price of ` 2200 per contract. The fund would
receive ` 5,00,000 being the excess of the selling price over the buying price
on 2500 Nifty futures. These additional funds can be used to compensate the
10 per cent increase in the prices of shares in the stock market. The mutual
fund can practically buy the same quantity of shares that it could have bought
one month earlier.
Imperfection in Hedging
Hedging may not be perfect always. This means that the gain in the futures
trading may not be sufficient to fully cover up the loss to be incurred. The
imperfections in hedging may arise from two sources. One source is the
difference in the value of the index and the price of the index future on any
day, which is known as basis. The possibility of there being such a difference
is known as basis risk. Basis risk is a source of imperfection in hedging.
In the case of the mutual fund discussed in the previous section, there is a
possibility that when Nifty stands at 2200, the Nifty futures price may be
only 2180. The mutual fund would be able to close out its long position only
at a selling price of ` 2180 per contract. It would thus receive only ` 4,50,000
in the futures transaction, whereas it requires ` 5,00,000 to compensate the 10
per cent increase in equity prices.
Similarly, there might be a difference in the percentage change in the value of
the portfolio being hedged and the percentage change in the index value. This
is another source of hedge imperfection. This is because the portfolio being
hedged has a beta value higher or lower than 1.0, which is taken as the beta
value of the index. The beta value, incidentally, is a measure of the change in
a share or a portfolio of shares in response to a change in the market index. A
balanced portfolio is likely to move in line with the stock market in general
and the market index. A stock or portfolio with only half the movement of the
market as a whole would have a beta of 0.5, while a portfolio with double the
degree of change in comparison to market movement would have a beta
value of 2. The beta value of a portfolio of shares is the weighted average of
the beta values of the shares constituting the portfolio.
Let us consider the earlier example of an investor who had a portfolio of
shares valued at ` 60,000. In order to hedge his risk in a declining or bearish
market, he took a short position in Nifty futures by selling 30 Nifty futures at
` 2000 per contract. If the percentage decline in share prices constituting the
portfolio is the same as the percentage decline in the value of the index, the
loss in the value of the portfolio would be exactly compensated by the gain
from the futures transaction. The hedge would be perfect. If, on the contrary,
the beta value of his portfolio is 1.2, the portfolio value will decline by 20 per
cent more than the decline in the index value. The gain from the futures
transaction would be insufficient to compensate fully the reduction in the
value of the portfolio. The hedge would be imperfect. In the earlier case, the
investor closed out his position when the index had declined by 10 per cent
and stood at 1800. He received a gain of ` 6000 from the transaction. If his
portfolio of shares has a beta value of 1.2, the value of his portfolio would
generally decline by 12 per cent when there was a general decline of 10 per
cent. As such the value of his portfolio would have declined to ` 52,800,
signalling a reduction in value to the extent of ` 7200. Thus, the gain of `
6000 would not fully compensate the reduction in value. In such situations,
the imperfection in hedge can be corrected by adjusting the number of index
futures to be bought or sold using the beta value of the portfolio or share to
be hedged.
The basic idea behind this strategy is that for hedging a portfolio with a
higher volatility than the market index, more futures contracts would be
required to bring about a perfect hedge. The required number of futures
contracts can be calculated by using the following formula:
In order to effect a perfect hedge, the investor would have to sell 36 Nifty
futures, if his portfolio has a beta value of 1.2. The gain from 36 Nifty futures
would be ` 7,200 (` 200 × 36 contracts), which would be sufficient to
compensate the reduction in the value of his portfolio.
While hedging a portfolio having lesser volatility than the index, lesser
number of futures is sufficient to effectively hedge the risk. The number of
futures required can be calculated using the above formula.
Speculation
Speculators may take short or long positions in index futures in order to gain
from the future movements in the stock index. For example, a speculator who
anticipates that there would be a decline in share prices, may take a short
position in the index future by selling the index future at its current price.
Later on, when the share prices have declined and the index value has
proportionately been reduced, he may close out his short position by buying
an equivalent number of index futures at the lower price prevailing in the
market. He makes a gain from the transaction.
Similarly, a speculator who anticipates a general rise in prices of shares
perceives an opportunity to make some profit. He then takes a long position
in the index future. Let us consider a speculator who buys 100 Nifty futures
at ` 1800 per contract when the Nifty value is at 1785, in the expectation that
share prices would shortly rise. If the share prices do rise as anticipated and
the Nifty value rises to 1965 within a month, the speculator can close out his
long position by selling 100 Nifty futures at the current price of ` 1965. He
would thereby make a profit of ` 16,500 being the excess of the selling price
over the buying price of 100 Nifty futures. The investment of the speculator
in this deal is the margin to be paid to execute the contract. Assuming that the
margin requirement is 12 per cent of the value of the contract, the speculator
would be required to pay ` 21,600 as margin for buying 100 Nifty futures at `
1800 per contract. On an investment of ` 21,600, he makes a profit of `
16,500 giving him a rate of return of about 76 per cent.
The stock index has risen from 1785 to 1965 within a month, signalling a rise
of about 10 per cent in share prices in the market. Had the speculator invested
the same amount of ` 21,600 in the share market for buying shares, he would
have gained only ` 2160 by selling the shares one month later at a higher
price, because the share prices have increased only by about 10 per cent
during the period.
As against the 10 per cent gain in dealing in shares, he makes a gain of 76 per
cent in the futures market by dealing in stock index futures. However, it may
be noted that the loss would be similarly different in both the markets, if there
is a decline in share prices against his expectations. This only shows that
speculating in the futures market is more risky.
Index Futures Trading in India
In year 2000, SEBI gave permission to NSE and BSE to trade index futures.
Trading of BSE Sensex futures commenced at BSE on 9th June 2000 and
trading of S and P CNX Nifty futures commenced at NSE on 12th June 2000.
Futures contracts on CNX IT Index (an IT sector index with 20 shares) are
also available for trading at NSE. Trading in stock futures or futures contracts
on individual stocks commenced later in 2001.
At any point of time there are only three contracts available for trading with
one month, two months and three months to expiry. These contracts expire on
the last Thursday of the expiry month. A new contract is introduced on the
next trading day following the expiry of the near month contract. For
example, at the beginning of May, the three contracts available for trading
would be those expiring in May, June and July. After the expiry of the May
contract on the last Thursday of May, a new contract expiring in August
would be introduced. The lot size for trading may be stipulated by the
exchange from time to time.
REVIEW QUESTIONS
1. Define a futures contract.
2. Distinguish between commodity futures and financial futures.
3. “The futures exchange specifies the terms of the contract.” Explain.
4. How is a futures contract different from a forward contract?
5. Write short notes on:
(a) Long position in futures contract
(b) Short position
(c) Open interest
(d) Variation margin
6. Describe the features of futures contracts.
7. Describe the facilities available in India for trading in futures contracts.
8. What is the margin system followed in futures trading?
9. What is marking-to-market?
10. What is meant by cash settlement of a futures contract?
11. What features provide liquidity to futures contracts?
12. How is default risk avoided in futures contracts?
13. What is an index future? How is it different from other futures
contracts?
14. Explain how index futures are useful in hedging risk.
15. How do imperfections in hedging arise? How can they be corrected?
16. “Speculators may take short or long positions in index futures to gain
from the future movements in the stock index.” Explain.
17. What facilities exist in India for index futures trading?
REFERENCES
1. Hull, John C., 1996, Options, Futures and Other Derivative Securities,
2nd ed., p. 3, Prentice-Hall of India, New Delhi.
2. Blake, David, 1992, Financial Market Analysis, p. 158, McGraw-Hill,
London.
21
OPTIONS
An option involves a choice. You have the option to either read this chapter
or not to read this chapter of the book. This is a free option. Neither do you
have to pay to have this option, nor are there any conditions attached to the
exercise of this option. You can exercise your option to read this chapter at
your own convenience and without anybody else’s consent.
However, all options are not free. At times, an option to do something may
have to be bought for a price, and it may be attached with certain conditions.
Such an option gives a right to the buyer of the option and it forms the
subject matter of an agreement or contract between the parties involved. This
is known as an options contract.
Financial options are typical examples of options contracts. They may relate
to individual stocks, stock indices, bonds, interest rates, currencies or futures.
And since they are based on and derived from underlying assets like
individual stocks, bonds, currencies, etc. they are also known as financial
derivatives.
STOCK OPTIONS (OPTIONS ON SHARES)
An investor who desires to buy a share may do so at the current market price.
By doing so, he foregoes an opportunity to buy the share at a lower price if
the price declines in the immediate future. On the contrary, by not buying the
share at the current market price, the investor exposes himself to the risk of
having to buy the share at a higher price if the share price rises in the
immediate future. The investor, in this case, can retain the opportunity to buy
the share at a lower price if the price declines and also hedge the risk of
having to buy at a higher price if the price rises. These twin objectives can be
achieved by entering into a stock options contract. He needs to buy a call
option.
CALL OPTIONS
There are two types of stock options: call option and put option. A call option
provides the right to buy a specified share at a specified price (known as the
strike price or exercise price) during a period of time (or at a point in time).
A put option gives an investor the right to sell the underlying share at the
exercise price before the expiry date. There are two parties to an options
contract: buyer of the option who gets the right to buy the specified share (in
the case of the call option) and the seller of the option who is prepared to sell
the specified share to the buyer of the option if he chooses to exercise his
right. The options contract is initiated by the seller of the option and hence
the seller of the option is known as the writer of the option, and the act of
selling an option is called writing an option. When the owner of a call option
chooses to buy the share underlying the option, he is said to “exercise the
option”.
Let us consider the share of the pharmaceutical company CIPLA, whose
current market price is Rs. 277. An options contract may be created on this
share and traded. A call option on the share would give the right to buy the
share at a specified price (for example, ` 280) during the next three months.
This call option would be traded between two parties P (the purchaser) and S
(the seller). The purchaser P would be prepared to pay a small price known as
option premium (` 10) to S, the seller of the option.
Specifications of Stock Options
Every option traded on an exchange is valid only for a limited period of time.
The period of validity of an option contract is known as its maturity or
expiration date. Based on the maturity pattern of options, option contracts
are categorised into European style options and American style options.
Options which can be exercised only on the maturity date of the option or the
expiry date are known as European style options. An American style option
can be exercised any time up to and including the expiry date. Most
exchange-traded options are American style. In India stock options are
American style while stock index options are European style.
There are two categories of options based on their mode of trading. These are
over-the-counter (OTC) options and exchange traded options. OTC options
result from private negotiations between two parties (typically, a bank and a
client). They may relate to any amount of any financial instrument at any
agreed price and can have any expiry date. In the case of OTC options,
financial institutions and corporate clients trade directly with each other and
the terms of the option contracts are tailored by a financial institution to meet
the specific needs of a corporate client. OTC options on foreign exchange and
interest rates are actively traded.
Exchange traded options are bought and sold on organised exchanges. There
are many such exchanges in existence in different countries. The Chicago
Board Options Exchange (CBOE) and the American Stock Exchange
(AMEX) are two such exchanges in the United States. Options are traded in
the futures and options segments of both the BSE and the NSE in India.
Trading in options on S and P CNX Nifty index commenced in June 2001.
Trading in options on shares started in July 2001. The exchange traded
options are standardised as to the amount and exercise price of the underlying
instrument, the nature of the underlying instrument and the available expiry
dates. Option contracts would relate to discrete blocks or quantities of the
underlying instrument and would provide a limited range of exercise prices
and expiry dates.
All the call options on a particular underlying stock constitute a class of
options. Similarly, all the put options on the same underlying stock would
constitute another class. Within each class there will be a number of series.
For example, all call options on a particular stock with the same expiry date
would constitute a series. At any given time, option series with three expiry
dates will be available for trading; one expiring in the near month, another in
the next month and the last expiring in the third month. At the beginning of
May, the three option series available for trading would be those expiring in
May, June and July. The last Thursday of the month is the expiry date for
option contracts in India. On the day after the expiry date of the current
month option series, another option series expiring in the month after the
third month would be listed for trading. On the day after the expiry date of
the May option series, August option series would be listed for trading.
In an option series expiring in a particular month, a series of strike prices are
listed for trading. The premiums quoted for options with different strike
prices would vary depending upon the spot price or the current market price
of the underlying stock.
Option Prices in the Newspapers
Many financial newspapers carry option quotations. These include the name
of the company on whose share options are traded, the closing share price,
the exercise price of the option and also the prices of the options (or option
premiums). The option prices are determined by market forces and may vary
from day to day.
Here are some premium quotations from the National Stock Exchange of
India for stock options traded there, as on the close of trading on 23 May,
2005.
ONGC Call Options
Spot price: ` 877
Exercise
price
Lot size: 300
Premium
May
June
July
800
61.35
15.00
NA
820
35.00
NA
NA
840
27.40
49.00
NA
860
16.00
26.00
NA
880
6.50
15.00
NA
900
2.00
NA
10.00
920
1.20
7.00
NA
NA = Not Available
ONGC Put Options
Spot price: ` 877
Exercise
Lot size: 300
Premium
price
May
June
July
800
1.00
NA
NA
820
2.00
NA
NA
840
1.80
NA
NA
860
2.75
20.00
NA
880
13.10
NA
24.00
900
35.00
NA
NA
920
NA
NA
NA
ICICI Bank Call Options
Lot size: 700
Spot price: ` 401
Exercise
Premium
price
May
June
July
350
46.00
NA
NA
360
35.00
NA
NA
370
34.00
NA
NA
380
21.00
NA
NA
390
12.70
NA
NA
400
5.00
13.50
NA
410
0.55
NA
NA
420
1.20
NA
NA
430
1.20
NA
NA
Cipla Call Options
Spot price: ` 273.50
Exercise
price
Lot size: 1000
Premium
May
June
July
230
18.00
NA
NA
240
25.00
NA
NA
250
23.05
NA
NA
260
11.00
NA
NA
265
10.20
NA
NA
270
4.95
10.00
NA
280
1.15
6.20
NA
290
1.00
2.10
NA
300
1.00
NA
NA
TRADING IN CALL OPTIONS
A call option is a contract that gives the owner the right, but not the
obligation, to buy something at a specified price on or before a specified date.
It may be noted that the buyer of the call option has the right to buy or not to
buy the specified asset, whereas the writer of the call option has the
obligation to sell the specified asset if the buyer of the option exercises his
option to buy the asset. Let us, therefore, see when the owner of a call option
on shares would prefer to exercise his option and what benefit he gets out of
it.
Let us specify certain notations. The exercise price or strike price may be
denoted as K. The expiry date of an option may be denoted as T. The price of
the underlying asset may be denoted as S. The call option’s price (referred to
as option premium) may be denoted as C. Frequently, time subscripts may be
necessary for S and C. The subscript ‘0’ will be used to refer to current time
(that is, today). Other time subscripts that will be used are T for the option’s
expiration date and t for some date between today and expiration date.
Option contracts are created when a buyer and a seller (or writer) agree on a
price (or option premium) for the options available for trading. The buyer
then pays the premium to the writer. The buyer becomes the owner of the
option and he has time till the expiration date to exercise the option.
Let us consider an investor who has purchased a call option on Satyam with
exercise price at ` 280 for a premium of ` 10. If the price of the share rises
above ` 290 at any time before the expiry date, the owner of the option may
exercise his option to buy the share at ` 280 and the writer would be obliged
to make the share available to the owner of the option at the exercise price.
The call owner can then make a profit by selling the share immediately in the
share market at the prevailing market price. Let us assume that the current
market price of Satyam is ` 350. If the call option owner exercises the option
to buy the share at the exercise price of ` 280, he would be able to make a
gross profit of ` 70 (` 350 − ` 280) and a net profit of ` 60 (` 70 − ` 10).
Hence, it would be profitable for the owner of the call option to exercise his
option if the current market price of the share is greater than the sum of the
exercise price and the option premium, that is if S > (K + C). As there is no
limit to the increase in share price, the profit potential of the owner of a call
option is limitless.
If the market price of the share underlying the call option does not rise above
the exercise price before the expiration date, there is no logic in exercising
the option. He can buy the share from the market at a lower rate. Hence the
owner of a call option will not exercise his option if K > S. The option will
lapse unexercised. Since he has already paid the option premium, that would
be a loss to him. Thus, the maximum loss that a call option owner has to
incur is limited to C, the option premium. The profit potential of a call option
owner is limitless, but the maximum loss is limited to the premium paid to
buy the option.
Profit and Loss of a Call Option Writer
It may be observed that the call option writer has the obligation to sell the
underlying asset to the owner of the option at the exercise price, if the owner
chooses to exercise his option. The call option writer may write a call option
without owning the underlying asset, in which case he is said to have written
a naked call. If the owner of such a call exercises the option, the writer will
have to buy the share from the market at the prevailing market price and sell
it to the owner of the call at the exercise price which would be lower than the
prevailing market price. The gross loss of the writer would be equal to the
difference between the current market price and the exercise price, that is, (S
− K). As the writer has already received the option premium at the time of
entering into the option contract, his net loss would be the gross loss minus
the option premium, that is, (S − K − C). In cases where the call writer owns
the underlying asset when he writes the call, he is said to write a covered
call.
In an option trading contract, profit accrues to the call writer when the call
lapses unexercised. In such a case the profit available to the writer is the
option premium received from the buyer of the option. Thus, the maximum
profit available to a call writer is limited to the option premium; while the
loss may be limitless.
Option trading is a zero sum game. The gain of the call owner or buyer is the
loss of the call writer; the loss of the call owner is the gain of the call writer.
Determinants of the Option Premium
The option premium is the amount paid by the buyer to buy the option and
represents the worth or value of the option. Let us see what factors determine
the option premium.
A call option buyer buys the option to be able to exercise it and make a profit.
The call option will be exercised and will yield profit to the owner only if the
current share price is greater than the exercise price. Hence, a call option is
said to be in the money if the current share price is greater than the exercise
price. At any time t before the expiration date, an option may be in the
money, at the money or out of the money.
A call is at the money when the share price equals the exercise or strike
price. A call is out of the money, when the share price is less than the
exercise price. Thus, for a call option:
If St > K, it is in the money.
If St = K, it is at the money.
If St < K, it is out of the money.
If an in-the-money call option is exercised immediately, it would result in a
positive cash flow to the holder. This positive cash flow or the gross profit
accruing to the holder is known as the intrinsic value of the call. For
example, consider a call option with exercise price ` 250. When the share
price is ` 310, the call option is in the money. If the owner of the call were to
exercise it, he would get a gross profit of ` 60 (` 310 − ` 250). This is the
intrinsic value of the call at the moment. An at-the-money option would lead
to zero cash flow if it were exercised immediately. In this case, when the
share price is ` 250, the call is at the money. If the owner of the call were to
exercise it immediately, he would get no cash flow. Similarly, an out-of-the
money option would lead to a negative cash flow if it were exercised
immediately.
The intrinsic value of a call option is the amount of the option in the money,
if it is in the money. If the call is at the money or out of the money, the
intrinsic value is zero.
This means the intrinsic value of a call is the greater of 0, or (St − K).
The option premium or price of the option depends upon the intrinsic value of
an option. The price of an in-the-money option must be at least as much as its
intrinsic value since the holder can realise the intrinsic value by exercising it
immediately. But it is optimal for the holder of an in-the-money option to
wait rather than exercise it immediately, because by waiting he may be able
to realise higher profit in the future. For example, the holder of a call option
which is in the money can realise the intrinsic value (St − K) immediately by
exercising it. But, if he waits, there is a probability that the share price may
increase further in the future and he may be able to realise a higher profit
then. Thus waiting for the future has a potentiality of increasing the profit
expected from an option contract. The option is then said to have time value.
The total value of an option or the option premium payable would therefore
be the sum of its intrinsic value and its time value.
An option’s price or premium can be broken down into two parts: intrinsic
value (sometimes called parity value) and time value (sometimes called
premium over parity). The time value of an option is the excess of the
premium over its intrinsic value. Let us consider an example. The premium
quoted for a call option with strike price ` 180 is ` 10. If the current market
price of the share underlying the option is ` 186, the call option is in the
money. The intrinsic value of the call is ` 6 (St − K). The premium quoted
being ` 10, the excess of the premium over the intrinsic value (` 4) is the time
value of this call option.
A call that is at the money or out of the money, has no intrinsic value. It has
only time value and the entire premium represents the time value. For
example, consider a call with strike price ` 180. When the price of the share
underlying the call is ` 173, the call is out of the money and there is no
intrinsic value. If the premium currently quoted for the option is ` 5, this
premium represents the time value of the option. This is the result of the
expectation that, in future, the option will become an option in the money
with increase in the share price.
A call that is currently in the money may, or may not, have time value. An inthe-money call will have time value if the premium payable for it exceeds its
current intrinsic value, that is, if Ct > (St − K). An in-the-money call will have
no time value if the premium payable equals its intrinsic value, that is, if Ct =
(St − K). Thus,
The time value of a call = Ct − {max [0, (St − K)]}
The determination of the option premium depends upon calculation of the
intrinsic value and estimation of the time value. The intrinsic value of a call
option can be calculated easily. It is equal to the current share price minus the
exercise price of the call option, with zero being the minimum intrinsic value.
However, the estimation of the time value is more complex. The major
factors influencing the time value of an option are the expected volatility of
the share price, the length of the period remaining to the expiry date and the
extent to which the option is in or out of the money.
The higher the expected volatility of the share underlying an option, the
greater will be its time value and the premium. This is because an option on a
volatile share has a strong chance of acquiring intrinsic value at some stage
prior to expiry. Similarly, the probability of an option acquiring intrinsic
value prior to expiry rises with the length of time remaining to its expiry date.
Hence, options with distant expiry dates have higher ime values and
premiums.
Whether an option is in the money or out of the money also influences its
time value. The time value of an option would be at its peak when the option
is at the money and it declines as the option moves either into or out of the
money. Out-of-the-money options have less time value than at-the-money
options because the share price has to move further before intrinsic value is
acquired. Similarly, in-the-money options have less time value than at-themoney options. This is because an in-the-money option already has an
intrinsic value which is vulnerable to a fall in the share price. The risk that the
existing intrinsic value might be lost due to a fall in share price reduces the
attractiveness of the option and lowers its time value and premium.
PUT OPTIONS
“A put option gives its holder the right, but not the obligation, to sell shares at
a specified price, prior to, or on the expiry date of the option.”1 An investor
buying a put option gets the right to sell the underlying share at the exercise
price before the expiry date. For example, an investor may purchase a put
option on ONGC share with a strike price of ` 850 and expiration in June, by
paying a premium of ` 25. The investor, in this case, has obtained the right to
sell ONGC share at ` 850 before the expiry date of the option. Whether he
will exercise the option depends upon the market price of ONGC share. If the
market price of the share moves above the exercise price, it would not be
worthwhile to exercise the option of selling the share at ` 850, because he will
have to buy the share from the market at a higher price to exercise his option.
This would result in a loss to the investor. He would allow the option to
expire unexercised.
On the contrary, if the market price of ONGC share declines and falls to `
785 before the expiry date, the holder of the put option would find if
profitable to exercise the option. He would be able to buy the share at ` 785
and exercise his put option of selling it at ` 850. His gross profit would be `
65, being the difference between the selling price and the buying price of the
share. Since the put option was purchased by paying a premium of ` 25, the
net profit would be ` 40. Thus, for a put option:
If K > St, it is in the money.
If K = St, it is at the money.
If K < St, it is out of the money.
Hence, it would be profitable for the holder of a put option to exercise his
option, if the strike price (exercise price) is greater than the sum of the
current market price of the share and the option premium, that is, if K > (S0 +
C). As the market price of the underlying share declines, the profit of the
holder of the put option increases. For example, if the market price of ONGC
share declines to ` 700, the put option holder can exercise his option and
make a gross profit of ` 150 (` 850 − ` 700) and a net profit of ` 125 (` 150 − `
25).
Assuming that the share price may decline to zero, the maximum profit that
the holder of a put option can obtain is limited to (K − C), that is, the exercise
price minus the option premium. Accordingly, this is the maximum loss that
the writer (seller) of the put option may suffer.
When the market price of the underlying share exceeds the exercise price it
would not be profitable to exercise the put option and hence it will expire
unexercised. The holder of the option would lose the premium already paid.
Thus, his loss is limited to the option premium paid for buying the option.
When the put option expires unexercised, the writer of the option gains the
entire option premium. The maximum gain that the writer of a put option
may secure is limited to the option premium.
A put option yields profit to the holder only if the exercise price exceeds the
market price of the underlying share. When the exercise price is equal to or
less than the market price, there is no value to the holder of the put option.
Thus,
Intrinsic value of a put = {K − St, if K > St}
{0, if K < St}
Another way of denoting this is
Intrinsic value of a put = max [0, (K − St)]
The premium quoted for a put option may comprise of two elements, intrinsic
value and time value. A put option at the money or out of the money has no
intrinsic value; hence, the entire premium would represent time value. In the
case of a put option in the money, the time value would be the excess of the
premium over the intrinsic value which is (K − St). An in-the-money put
option will have no time value if the premium quoted equals its intrinsic
value, that is, if Ct = (K − St).
Thus, the time value of a put = Ct − {max [0, (K − St)]}
For every buyer of an option, there must be a seller. Profit of the buyer equals
the loss of the seller and vice versa. The buyer of a call option has unlimited
profit potential, but the loss is limited to the premium paid. Conversely, the
writer of a call option faces unlimited loss potential with maximum profit
limited to the premium received. In the case of put options, the loss of the
buyer is limited to the premium paid, while his maximum profit would be
equal to the exercise price minus the premium. For the seller of a put option,
the maximum profit would be the premium received, while his loss would be
limited to the exercise price minus the premium.
CLOSING OUT OF OPTIONS
An option contract gives the holder of the option the right to buy the
underlying share (in a call option) or the right to sell the underlying share (in
a put option) within a specified period. The holder of the option may exercise
the option if the price movement of the underlying share is favourable to him.
If the price movement during the specified period is unfavourable to the
option holder, he may allow the option to lapse without exercising it. In
options trading, the clearing house acts as the counter party in each option
contract. If the holder of an option chooses to exercise his option, the clearing
house through a random selection process chooses a writer who is assigned
the obligation of selling the share (in the case of a call option being
exercised) or buying the share (in the case of a put option being exercised).
The option holder has another alternative course of action. He can close out
his original contract by selling it to another party. The buyer of an option is
said to have a long option position, whereas the writer of an option is said to
have a short position. The long position of the buyer of an option can be
closed out by writing or selling an identical option.
Let us consider an investor who has purchased a call option expiring in
November on ICICI Bank share at an exercise price of ` 375, by paying an
option premium of ` 24. Subsequently, the share price rises to ` 420. The
investor may exercise his call option to buy the share at ` 375. He would
secure a gross profit of ` 45 (i.e. ` 420 − ` 375) and a net profit of ` 21 (` 45 −
` 24), by selling the share immediately at the current market price of ` 420.
Alternatively, he may close out his long position by selling the call option on
ICICI Bank share expiring in November and with exercise price ` 375. This
call option is now in the money and its intrinsic value is ` 45 (i.e. St − K). If
this call option has time value, the premium payable would be the total of the
intrinsic value and the time value. Let us assume that the premium quoted is `
52. The investor can sell the call option and receive the premium of ` 52
which would give him a net profit of ` 28 (i.e. ` 52 − ` 24).
Likewise, the writer of an option can close out of his short position by buying
an identical option. Most of the exchange traded options are closed out before
the expiry dates. A long option position (or option bought) is closed out by
the sale of an identical option. Short option positions (written options) can be
closed out by buying identical options. Since the clearing house takes the role
of the counter party to every option trader as soon as options are traded,
closing out need not be with the original counter party. An option trader can
close out his position by entering into an opposite transaction with any other
trader. The process of closing out option contracts will reduce the number of
contracts in existence.
The purchase of an option may be an opening purchase or a closing purchase.
An opening purchase is a transaction whereby the buyer of an option
becomes its holder, a closing purchase is a purchase transaction which is
entered into by the writer of an option to close out the option earlier sold by
him. A closing purchase cancels out an earlier sale. Similarly, the sale of an
option may be an opening sale or a closing sale. An opening sale is a
transaction in which the seller of the option has an open short position. A
closing sale involves the cancellation of a previously purchased option.
USES OF OPTIONS
“The ultimate economic function of financial derivatives (forwards, futures,
swaps and options) is to provide means of risk reduction. Someone who is at
risk from a price change can use options to offset that risk.”2 Hence, options
can be used as hedging instruments.
Options give the option holder the right to buy a share (call option) or the
right to sell a share (put option). The right may be exercised to secure a profit
when the price movement of the underlying share is favourable to the holder
of the option. An option contract is a derivative security which is traded in
the options exchange for a price known as option premium. The premium on
a particular option keeps on changing in response to changes in the price of
the underlying share. Hence, there is an opportunity for making gains by
buying and selling stock options in the derivatives market. A given per
centage change in the stock price will lead to a much greater per centage
change in the price of the option. Thus options offer a great deal of leverage.
Hence, speculators are attracted to the derivatives market by the exciting
speculative opportunities offered by trading in options. Options are used by
speculators to make speculative gains.
Hedging the Value of a Stockholding
A put option can be used to hedge the value of an existing stockholding. An
investor holding a particular stock faces the risk of reduction in the value of
his stockholding due to a decline in the price of the stock. This risk can be
effectively hedged with a put option. The investor can buy a put option at an
exercise price close to the current market price, thereby guaranteeing a selling
price for his stock, even if there is a fall in its market price later.
Let us consider an investor who has 500 shares of a company whose current
market price is ` 356. The value of his stockholding is ` 1,78,000. If there is a
fall in the price of his share, the value of his stockholding will decline. When
a fall in share prices is expected, the investor can buy put options on the stock
to hedge his risk. Let us assume that put option on the stock with exercise
price of ` 350 is available for a premium of ` 14. The investor can buy 500
put options on the stock by paying ` 7000 (i.e. ` 14 × 500) as premium.
Subsequently, let us assume that share price has declined to ` 296. As share
price declines, the intrinsic value of the put option on the share will increase,
being the excess of the strike price over the current market price. The
intrinsic value of the put option purchased by the investor would now be ` 54
(` 350 − ` 296). If there is more time to the expiration date, the put option
would have a time value also. Let us assume that there are 10 days to
expiration and the time value of the put option is ` 10; then the premium on
the put option purchased by the investor would be ` 64 (` 54 + ` 10), the
premium being the sum of the intrinsic value and the time value.
As the price of the share has come down to ` 296 from ` 356, there is a
decline in the value of the stockholding to the extent of ` 30,000. There are
two choices before the investor who has a put option on the stock with ` 350
exercise price. He may either exercise his put option or close out his long
position by selling the put option. If he exercises his right under the put
option to sell the shares at ` 350 per share, he would receive ` 1,75,000 as sale
proceeds, the reduction in value being only ` 3000. As he has already paid a
premium of ` 7000 to buy the put option, the total loss of the investor would
be ` 10,000. If he had not hedged his risk with a put option, the reduction in
the value of the stockholding would have been ` 30,000.
The second alternative before the investor with the put option is to sell the
option at its current premium of ` 64. He would receive a cash flow of `
32,000, being the sale proceeds of 500 put options at ` 64 per option. The
gain from the options trading would be ` 25,000, after deducting the cash
outflow for purchase of the options. Here, the investor retains the shares; the
reduction of ` 30,000 in the value of the stockholding is compensated to the
extent of ` 25,000 by the profit in options trading. The investor can choose
the course of action which is more advantageous to him.
If, on the contrary, the share price has increased instead of declining, the
value of his stockholding would increase accordingly. The put option will not
be exercised. However, the premium paid represents a loss to the investor
which may be compensated by the increase in the value of the stockholding.
Protecting Profit Accrued on Share
A put option can be used to protect the profit accrued on a share without
foregoing the opportunity to make larger gains in case of further increase in
share prices. Let us consider an investor who has purchased 1000 shares of a
company at ` 32 per share. The total investment in shares is thus ` 32,000. Let
us assume that the price of the share has gradually increased to ` 56. A profit
of ` 24 has accrued on the share. The investor can book the profit accrued on
the share by selling the shares at the current market price. Then he would be
foregoing the opportunity of making larger profits from further increases in
share prices. But, if he does not sell the shares to retain the opportunity of
making larger profits from future rise in share prices, he faces the risk of
losing the profit already accrued on the share through a fall in share prices in
future. The future movement of share prices is uncertain. The investor would
like to protect the profit already accrued on the share in case of a fall in
prices; he would also like to retain the opportunity of making more profits in
case of a rise in prices. The twin objectives can be achieved by buying a put
option at an exercise price close to the current market price.
Let us assume that put options with exercise price of ` 55 is available at a
premium of ` 4. The investor can buy 1000 put options paying a total
premium of ` 4000. If prices fall, he can exercise his put option to sell the
share at ` 55 per share. His profit per share would be ` 19 (i.e. ` 55 − ` 32 − `
4), whatever be the extent of fall in prices. He is thus able to protect ` 19 out
of the accrued profit of ` 24 per share.
Alternatively, the investor may retain the shares and may close out his option
contracts by selling the put options at a profit, to recover the loss due to
decline in the value of his shares. Let us assume that the share price has
declined to ` 40. There is a reduction in the value of his share to the extent of
` 16 (i.e. ` 56 − ` 40). The intrinsic value of the put option is `15, when the
market price is ` 40. Assuming the time value of the put option to be ` 5, the
option premium of the put option held by the investor would be ` 20. By
selling the put option at ` 20, the investor would make a profit of ` 16 (i.e. `
20 − ` 4). The erosion in the value of his shares to the extent of ` 16 is fully
compensated by the profit in options trading. The profit from options trading
would, however, depend on the premium at the time of closing out of the
option. In this case the investor compensates the erosion in value of his
shares from the profit obtained through options trading, but at the same time
retains the shares to benefit from future rise in share prices.
If, subsequent to the purchase of the put options, the share price rises, the
investor would not exercise his put option to sell the shares. He would lose
the premium paid for the put options, but would gain from the increase in
share prices.
Hedging Anticipated Purchases
Options can be used to hedge the risk involved in planned purchases of stock.
Investors and portfolio managers of investment companies often plan
purchases of shares in the future when some funds are expected to be
received. Meanwhile, if the share prices rise, they will be forced to pay higher
prices for their planned purchases of shares. The risk of having to pay higher
prices on account of a rise in share prices can be avoided or hedged by
buying a call option with exercise price close to the current market price,
thereby guaranteeing a buying price for the future planned purchase of
shares. Subsequently, if the share prices rise, the call option holder can
exercise his call option to buy the shares at the guaranteed price thereby
avoiding the possibility of having to pay higher prices for the purchase. Or
else, the option holder may sell the options at a profit and utilise the cash
flow to compensate the increase in share prices.
Sometimes, share prices may not rise as anticipated. Prices may remain the
same or may have declined. The investor or portfolio manager can make the
planned purchases at the same prices or lower prices, as the case may be. The
call options will not be exercised. However, the call options may be sold to
recover at least part of the premium paid, if the options have any time value.
Additional Income from Stockholding
Option trading can be used to make some additional income from existing
stockholdings through covered writing of options. Covered writing refers to
selling call options on shares held by the investor, or selling put options when
cash for the purchase of the underlying share is held by the investor.
A person writing a call option should be prepared to sell the underlying share
if the holder of the option exercises his right to buy the share. If the writer of
the call option does not own the share, he will have to buy it from the market
at the current market price to fulfil his obligation. A call option written
without owning the underlying share is called a naked call option. If, on the
contrary, the writer of the call option owns the underlying share, he can
surrender his share when the holder exercises his right to buy the share under
the call option. A call option written on a share owned by the writer is known
as covered call option.
Let us consider an investor who holds 500 shares of a company having a
current market price of ` 272. He anticipates a short-term decline in share
prices. He can utilise this situation to make some additional income from his
shareholding. He can write a covered call option on the shares held by him. If
the call option on the share with exercise price of ` 270 is quoted at a
premium of ` 12, the investor will receive ` 6000 as option premium by
selling 500 call options.
If the market price of the share declines below ` 270 (the exercise price) as
anticipated, the buyer of the call option will not exercise his right to buy the
share at ` 270, because the share is available in the market at a price lower
than ` 270. The investor who has written the call option appropriates the
premium received as his profit. He thus gains an additional income through
writing of a covered call option.
If the price of the share rises above ` 270 against the anticipation of the
investor, the buyer of the call option is likely to exercise his right to buy the
share at ` 270. But, then, the investor need not buy the share from the market
at a higher price to sell at ` 270 and incur a loss in the transaction. He can
surrender his shareholding to fulfil the obligation under the call option.
Speculative Profit from Options Trading
Options are derivative securities which can be bought and sold in the
derivatives market. The price of an option contract is the premium. The
premium depends upon the intrinsic value and the time value of the option.
The premium or price of an option keeps on changing as the price of the
underlying share changes. The fluctuations in the premium of option
contracts provide an opportunity to speculators to make gains in options
trading. A speculator may buy an option at a low premium and sell it later at
a higher premium to make short-term gains.
Even though the primary function of options is to provide a means for
hedging the risk arising from price fluctuations of shares, options can also be
used for making short-term gains from the price fluctuations.
Let us consider an example. The current market price of a share is ` 63. An
increase in the price of the share is anticipated. This provides an opportunity
for making short-term gains from the anticipated price movement. A person
may buy 100 shares at ` 63 per share and wait for the share price to rise. Later
on, he may sell the shares at ` 86. The profit per share amounts to ` 23. He
thus makes a profit of ` 2300 on an investment of ` 6300 for 100 shares. The
rate of return works out to 36.5 per cent.
In this case, it is not necessary to buy the shares outright. A person may buy a
call option at an exercise price close to the current market price. This gives
the holder the right to buy the share later at the exercise price. The option can
be purchased by paying the premium. The advantage here is that the
investment required is limited to the premium.
Let us assume that 100 call options are purchased by the trader with an
exercise price of ` 65 for a premium of ` 5 per option. The total investment
for purchasing 100 call options comes to ` 500 only. When the share price
rises to ` 86, he can exercise his right to buy the share at ` 65 and sell them
immediately for ` 86 and thereby make a profit of ` 16 per share (i.e. ` 86 − `
65 − ` 5). The total profit on sale of 100 shares would be ` 1600 on an
investment of ` 500 as premium, giving him a rate of return of 320 per cent.
Alternatively, he may sell the call option which was purchased for ` 5 at its
current premium of ` 23, giving him a higher profit of ` 18 per share (i.e. ` 23
− ` 5).
Here we have seen that by buying and selling the share itself, the trader
makes a return of only 36.5 per cent. But a trader buying and selling the call
option on the share, in the same situation, can make a return of 320 per cent.
It is thus more attractive to trade a derivative security than the security itself,
because with small investment, large profits can be made. When an increase
in share price is anticipated, a trader may buy a share or he may buy a call
option on the share. The latter choice gives higher returns.
But it may be remembered that the risk would also be higher in derivatives
trading compared to trading in the security itself. In the example cited above,
if the share price were to decline by ` 23, the trader who purchased the share
would suffer a loss of 36.5 per cent, but the trader who bought the call option
would not exercise the call option when the market price falls below the
exercise price and thereby would be losing the entire premium paid. His loss
would be 100 per cent as against the loss of only 36.5 per cent of the trader
who bought the share itself.
Options may be used for making speculative profits as well as for hedging.
Call options can be used to hedge future purchase of the underlying share by
guaranteeing a maximum buying price; while put options can be used to
hedge against a fall in prices by guaranteeing a minimum selling price for the
underlying share. Similarly, options may be written so as to utilise the
premium receipts to compensate the loss on account of adverse movements in
prices of shares.
The use and profit payoffs of the investment in a single stock option were
explained and illustrated in this chapter. Options can be used to create a wide
range of different payoff functions, by combining different options on the
same stock or by combining a position in a stock option with a position in the
stock itself. Accordingly, a number of different trading strategies may be
used for hedging as well as speculative trading.
REVIEW QUESTIONS
1. What is a call option?
2. Write short notes on:
(a) Exercise price
(b) Option premium
(c) OTC options
(d) At-the-money call option
3. Distinguish between European style and American style options.
4. Distinguish between OTC options and exchange traded options.
5. “The profit potential of the owner of a call option is limitless.” Explain
and illustrate.
6. Describe the circumstance in which call option on shares will not be
exercised by the owner. Also discuss the consequences of a call option
remaining unexercised.
7. “The maximum profit available to a call writer is limited to the option
premium; while the loss may be limitless.” Explain.
8. What is an in-the-money call option?
9. What is the intrinsic value of a call option? How is it calculated?
10. What is meant by time value of a call option? Describe the factors
influencing the time value of an option.
11. What is a put option? Explain how the intrinsic value and the time
value of a put option are estimated.
12. Discuss the profit and loss accruing to the buyer and seller of a put
option.
13. Explain how options can be closed out.
14. What are the uses of options?
15. Explain how options can be used to hedge the value of a stockholding
against decline in share prices.
16. “A put option can be used to protect the profit accrued on a share.”
Explain.
17. Discuss how options can be used to hedge planned purchase of shares
in the future.
18. Explain how covered writing of options can be used to gain additional
income from stockholding.
19. “It is more attractive to trade a derivative security than the security
itself.” Discuss.
20. Illustrate, with an example, the use of options trading for speculative
gains.
REFERENCES
1. Rehead, Keith, 1998, Financial Derivatives, p. 157, Prentice-Hall of
India, New Delhi.
2. Ibid., p. 178.
22
OPTION PRICING
An option is the right to buy or sell a specified asset for a limited period at a
specified price, known as the exercise price. The two classes of options are
call options (giving the right to buy the specified asset) and put options
(giving the right to sell the specified asset). The right is available only for a
limited period; the right is lost or expires after the specified maturity period.
The owner of the option has to exercise the right conferred by the option
before the expiry date.
The profitability of an option on a specified stock depends upon the
relationship between the exercise price of the option and the spot price of the
underlying stock. For example, a call option is profitable when the spot price
exceeds the exercise price, because the holder of the call option can buy the
stock at the lower exercise price and sell it at the higher spot price. As the
spot price of the underlying stock keeps on fluctuating from time to time, the
profitability of the option also changes. An option that is profitable at a
particular time is said to be in-the-money at that time. Similarly, the option
may be out-of-the money (giving a loss) or at-the-money (without profit or
loss) at other times depending upon the movement in the spot price of the
underlying stock.
Options are traded between interested parties either in the futures and options
exchanges or in over-the-counter deals. The buyer purchases the option from
the seller for a price known as option premium. The price is market
determined and is based on the perceived value of the option at the time of
trading. The perceived value of the option in turn depends upon certain key
variables.
In this chapter we focus on the option pricing process. We try to understand
the important variables that influence the option pricing process. We discuss
the alternative mathematical models that are being used for determination of
option prices.
Two models have been developed for option pricing. These are: (i) the BlackScholes model, and (ii) the Binomial model.
THE BLACK-SCHOLES MODEL
Most options traders have heard of the Black-Scholes model but few really
know much about it. The Black-Scholes model was developed in 1973 by
Fisher Black and Myron Scholes. In the same year, they published paper in
the Journal of Political Economy under the title “The Pricing of Options and
Corporate Liabilities”. Robert C. Merton published a follow up paper further
expanding the understanding of the model. Merton and Scholes received the
1997 Nobel Prize for their work. Fisher Black was ineligible because he had
passed away earlier and the Nobel prizes are not awarded posthumously.
Factors Affecting Option Prices
The Black-Scholes model has identified six factors affecting the price of a
stock option. These factors are:
1. The current stock price (S0)
2. The strike price or Exercise price (K)
3. The time to expiration (T)
4. The volatility of the stock price (σ)
5. The risk free interest rate (r)
6. The dividend expected during the life of the option (D)
These factors influence the value of an option in different ways. We shall
now see how each of these factors affect the value or profitability of options.
Current Stock Price and Exercise Price
In the case of a call option, the profit or payoff accruing to the holder is the
excess of the current stock price over the exercise price. Accordingly, call
options become more valuable as the stock price increases and less valuable
as the exercise price increases. For a put option, the payoff to the holder is the
amount by which the strike price exceeds the current stock price.
Accordingly, put options become more valuable as the strike price increases
and less valuable as the stock price increases. Thus, changes in the stock
price and the exercise price have opposite effects on the value of the options.
Time to Expiration
An option with longer life (or longer time to expiration) will have more value
than a similar option with a shorter life, because the long-life option has more
time and opportunities to become profitable than a short-life option. Thus,
options become valuable as the time to expiration increases.
Volatility of the Stock Price
Volatility gives rise to wide fluctuations in stock prices. There may be a
sharp rise or a steep fall in stock prices. The owner of a call option benefits
from rise in the stock prices. But, even in case of a decline in the stock prices,
the loss is limited to the premium. Hence, volatility enhances the probability
of getting higher payoffs from call option. Similar is the case with a put
option. The owner of a put option benefits from decline in the stock prices.
But, even when the stock prices rise, the loss is limited to the premium paid.
Thus, both call options and put options become more valuable as volatility of
the underlying stock increases.
Risk Free Interest Rate
Normally, as interest rates in the economy rise, stock prices tend to fall. A
decline in stock prices will reduce the value of a call option and enhance the
value of a put option. A fall in interest rates in the economy will be
accompanied by a rise in stock prices which, in turn, tends to enhance the
value of a call option and reduce the value of a put option. Thus, changes in
interest rates in the economy have an impact on the value of both call and put
options.
Dividends During the Life of an Option
On the ex-dividend date, the stock price declines to the extent of the dividend
paid. Such reduction in stock price on account of dividend reduces the value
of the call option, but enhances the value of the put option. Thus, anticipated
dividends during the life of an option have a positive effect on put option and
a negative effect on call option.
Assumptions
The Black-Scholes Option Pricing Model (BSOPM) takes into consideration
the impact of all the above factors on the value of an option and attempts to
determine the theoretical price of an option. The model presents a theoretical
formula for calculating the price of a call option. If we know the values of the
variables listed above, we can use the Black-Scholes pricing model to
calculate the theoretical price of an option. The analysis makes certain
assumptions regarding the market environment in which option trading takes
place. The assumptions are stated below:
1. There are sufficient numbers of market participants to ensure continuous
trading.
2. There are no transaction costs or the transaction costs are insignificant.
3. All trading profits are subject to the same tax rate.
4. Borrowing and lending are possible at the risk free interest rate, which
remains constant.
5. There are no arbitrage opportunities or arbitrage opportunities disappear
quickly.
6. There are no dividends on the stock during the life of the option.
7. Stock prices follow a random walk. It implies that the stock price at any
future time has a lognormal distribution, i.e. its natural logarithm is
normally distributed.
Notations
The following notations are used in the option pricing model.
S0 = Current stock price
K = Exercise price of option
T = Time to expiration of the option
r = Continuously compounded risk free rate of interest for an investment
maturing in time T
ST = Stock price at option maturity
c = Value of European call option to buy one share
p = Value of European put option to sell one share
The Pricing Formulas
The Black-Scholes option pricing model applies to European options on nondividend paying stocks buy adjustments can be made to the basic model to
deal with other cases. The Black-Scholes formulas for calculating the prices
of European calls and puts on non-dividend paying stocks are:
The cumulative normal probability value (N) for different values of d1 and d2
can be taken from the Cumulative Normal Distribution tables which provide
these values. These tables are provided in the Appendix to the chapter.
Natural logarithm values can be obtained from the logarithm table. It is also
provided in the Appendix.
The powers of e for different positive and negative values are available in the
table given in Appendix.
Use of Statistical Tables
BSOPM requires the following values for calculation:
1. Natural logarithm
2. Power of e
3. Cumulative normal probability value
These values are available in ready-made statistical tables which are given in
the standard textbooks. However, the statistical tables provide the values only
for certain discrete variables. But we may have to find these values (natural
logarithm, power of e, etc.) for continuous variables. In such cases, the values
may be obtained through interpolation.
An example would illustrate the use of interpolation for obtaining values for
continuous variables. In the BSOPM, we may be required to find the natural
logarithm of 1.0724. From the statistical table of Natural logarithm values,
we will get the natural logarithm values of 1.07 and 1.08.
These are as follows:
ln(1.07) = 0.06766 ln(1.08) = 0.07696
The natural logarithm value of 1.0724 lies between these two values. It can
be obtained through interpolation as shown below:
ln(1.0724) = ln(1.07) + 0.24 [ln(1.08) − ln(1.07)]
= 0.06766 + 0.24 (0.07696 − 0.06766)
= 0.06766 + 0.00223 = 0.06989
Similar interpolation procedure has to be carried out for finding the powers of
e and cumulative normal probability values for continuous variables.
The application of the Black-Scholes option pricing model (BSOPM) for
calculating option prices can be illustrated through examples.
SOLVED EXAMPLES
Example 1 He current market price of a share is ` 64. The volatility of the
share is measured as 25 per cent. The risk free interest rate is currently 8 per
cent per annum. There is a call option as well as a put option on the share,
expiring in six months, with exercise price of ` 60. Calculate the price of the
call option and the put option.
The last step is the final calculations, using the BSOPM formula.
c = S0N(d1) − Ke−rTN(d2)
= (64 × 0.7517) − (60 e−(0.08)(6/12) × 0.6926)
= 48.11 − 39.93 = 8.18
Calculation of the price of put option
p = Ke−rTN(−d2) − S0N(−d1)
Here, we have to identify the values of N(−d2) and N(−d1). These may be
taken directly from the Cumulative Normal Distribution table. Alternatively,
they may be determined as shown below:
N(−d1) = 1 − N(d1) = 1 − 0.7517 = 0.2483
N(−d2) = 1 − N(d2) = 1 − 0.6926 = 0.3074
Now we can do the final calculations.
p = (60 e−(0.08)(6/12) × 0.3074) − (64 × 0.2483)
= 17.72 − 15.89 = 1.83
Calculation of Put Option Price using Put-call Parity
In a well-functioning market, the options would be priced in such a way as to
yield no arbitrage opportunities. The option prices must satisfy certain criteria
in order to prevent arbitrage opportunities in the market. One such criterion is
the Put-call parity. This is an arbitrage restriction on option pricing. The
parity is stated as follows:
C − P = S0 − Ke−rT
This proposition states that the difference between the price of a call and the
price of a put on the same stock, with the same strike price and time to
expiration, equals the price of the underlying stock minus the present value of
the strike price (calculated using continuous compounding).
From the put-call parity, the put option price can be calculated easily.
Rearranging the put-call parity and solving for P, we get:
P = C − S0 + Ke−rT
With the data in Example 22.1, we can now calculate put option price using
Put-call parity.
Given/Calculated:
S0 = ` 64
C = 8.18
Ke−rT = 60 e−(0.08)(6/12)
= 57.65
Now P can be calculated:
P = C − S0 + Ke−rT
= 8.18 − 64 + 57.65 = 1.83
Dividends Anticipated during the Life of an Option
Black-Scholes option pricing model was developed on the assumption that no
dividends are received on the stock during the life of the option. The model
can also be used to cover cases where dividends are expected to be received
before the expiry date of the option. It is assumed that the dividends to be
received on the stock during the life of an option can be predicted or
estimated with certainty. On the ex-dividend date, the stock price normally
declines by the amount of the dividend paid, reducing the value of call
options and increasing the value of put options.
In the BSOPM, the current stock price is one of the variables used for
calculating the option price. In the cases where dividends are expected to be
received before the expiry of the option, the current stock price, S0, has to be
reduced by the present value of all dividends to be received during the life of
the option, using continuous discounting at the risk free rate. The present
value of the dividends can be calculated as follows:
De−rt
where
D = amount of dividend anticipated
e = 2.7182818
r = risk free interest rate
t = time to receipt of dividend
Example 2 The stock underlying a European call option is expected to pay
two interim dividends of ` 6 and ` 8 after 3 months and 6 months from now,
respectively. The risk free interest is 8 per cent per annum. Calculate the
present value of the dividends.
Solution The present value of dividends using continuous discounting is
given by the formula:
De−rt
Applying the formula for the two dividends expected after 3 months and 6
months, we get:
= 6e−(0.08)(2/12) + 8e−(0.08)(6/12)
= 13.5675
Thus, for calculating option price in a case where dividend is anticipated on
the underlying stock, the current stock price (S0) in the formula has to be
adjusted by deducting the present value of the dividend from the stock price.
Example 3 Options are available in the market on a stock whose current
market price is ` 140. The options expire in 8 months. The exercise price of
the option is ` 130. The volatility of the stock price has been ascertained as 32
per cent. The risk free interest rate is 8 per cent per annum.
Calculate the call option and put option prices:
(a) When no dividends are expected during the option life.
(b) When a dividend of ` 6 is expected to be received after 6 months from
now.
(b) Calculation of call option and put option prices when dividend is
expected
Here the current market price or spot price (S0) of the underlying stock has to
be adjusted by deducting the present value of the dividend to be received
during the life of the option.
Pricing of American Options
An American option is different from a European option only with respect to
the time when the option can be exercised by the holder or owner of the
option. A European option can be exercised only on the expiry date; while an
American option can be exercised at any time prior to expiry of the option.
Even though an American option can be exercised at any time prior to expiry,
it is not optimal to exercise an American call option on a non-dividend
paying stock before the expiration date. It would be desirable to wait till the
expiration date to take advantage of any favourable developments. Hence, in
practice, an American call option on a non-dividend paying stock will be
exercised only on expiration. This makes such an American call option
similar to a European call option on non-dividend paying stock. Hence, if
there are no dividends, the basic BSOPM can be used to calculate the prices
of both European as well as American call options.
However, when dividends are paid, it becomes optimal to exercise an
American call option just before payment of dividend, i.e. just before the
stock becomes ex-dividend. This is because, on payment of dividend, the
stock price would decline and reduce the value of the call option. Hence, in
practice, an American call option on a dividend paying stock will be
exercised early, i.e. just before the ex-dividend date (the last ex-dividend date
if more than one dividend is paid during the life of the option).
Fischer Black has suggested an approximate procedure for valuing American
call options on dividend paying stocks that are likely to be exercised early.
Black’s approximation involves calculating the prices of two options
maturing on two different dates:
1. An option maturing at the final expiration date of the option.
2. An option maturing just before the latest ex-dividend date that occurs
during the life of the option.
These calculations are made using the BSOPM formula for dividend paying
stocks. The American call option price should be taken as the higher of these
two prices.
An American put option on non-dividend paying stock that is out-of-the
money (not profitable) is not likely to be exercised early or prior to the
expiration date. In such cases, the BSOPM can be used to calculate the option
price. When an American put option is in-the-money, the probability of early
exercise is higher. It is optimal to exercise an American put option at the time
when it is sufficiently deep in-the-money. Hence, the value of an American
put option in-the-money is considered to be higher than the value of a
corresponding European put option.
American put options on dividend paying stocks are most likely to be
exercised immediately after the ex-dividend date, because the put option is
likely to be more valuable on that date. Black’s approximation procedure,
used in the case of American call options, may be applied to American put
options on dividend paying stocks. Several other approximation techniques
have also been developed to value American puts. These are beyond the
scope of this book.
BINOMIAL MODEL OF OPTION PRICING
A useful model of stock option pricing has been developed by Cox, Ross and
Rubinstein in 1979, using the concept of the binomial tree. The price of the
stock underlying an option may follow different paths in the future. It may
rise or fall. The different paths likely to be followed by the stock price may
be represented in the form of a diagram which is known as a binomial tree of
future stock prices.
Let us start by considering a very simple example. The current market price
of a stock is ` 60. It is expected that the price may either move up by 10 per
cent or move down by 10 per cent by the end of the month. This may be
represented in the form of a diagram (Fig. 22.1).
From the diagram it can be seen that at the end of the period, the stock price
may be ` 66 or ` 54. The probability of the upward movement and the
downward movement may be different. If the probability of the upward
movement is 0.6, then the probability of the downward movement would be
0.4 (i.e., 1 − 0.6). Now let us consider a European call option with exercise
price of ` 62, expiring at the end of the month. If the stock price at the end of
the month is ` 66, the option will have a value of ` 4 (` 66 − ` 62). If the stock
price is ` 54, the call option will have no value as the exercise price exceeds
the stock price; the option value would be 0. In Fig. 22.2 below, the possible
option prices at the end of the period are shown.
Since we know the probability of the upward and downward movements, we
can calculate the expected option value at the end of the period. This is the
probability weighted average of the possible option values. This is calculated
as follows:
Expected option value = (4 × 0.6) + (0 × 0.4) = ` 2.40
The expected option value at the end of the month is worked out as ` 2.40.
The present value of this amount is taken as the current price of the option.
The amount has to be discounted with the risk free rate using continuous
discounting process.
The formula is: 2.40 e−rT
Assuming risk free rate of 12 per cent per annum, the calculation is as
follows:
2.40 e−(0.12)(1/12) = (2.40 × 0.99005) = ` 2.376
Thus under the binomial option pricing model (BOPM), the current option
price is taken as the discounted weighted average of possible future option
values.
We can now extend the diagram into a two-step binomial tree where, at each
step, the stock price may either move up by 10 per cent or move down by 10
per cent. The extended diagram is shown below Fig. 22.3.
There are three possible stock prices at the end of the period 2, namely, `
72.6, ` 60, and ` 48.6. The binomial tree may be extended in a similar fashion
to several steps or time intervals.
In the case of binomial trees with more than one step, the option values at the
final nodes are calculated first. The current price of the option is determined
by working backward. This process is known as backward induction. From
the option values at the final nodes, the option values at the preceding nodes
are calculated. The option values at previous nodes are calculated as the
present value of the expected option value one time step later.
The Model
The basic assumptions underlying this model is that stock price movements
are binomial in a short period of time of length ‘t’. We start by dividing the
life of the option into a large number of small time intervals of length ‘t’. We
assume that in each time interval the stock price moves from its initial value
of S to one of two new values, Su and Sd. In general, u > 1 and d < 1. The
movement from S to Su is an up movement and the movement from S to Sd is
a down movement. The probability of an up movement is assumed to be p
and the probability of a down movement is assumed to be (1 − p); see Fig.
22.4.
Determination of p, u and d
We assume that the world is risk neutral. Hence, the expected return from a
stock is the risk free interest rate, r. The volatility of the stock returns is
determined by the variance of the change in stock prices. The values of u, d
and p can be determined by using following formulas.
The Tree of Stock Prices
Using the values of u and d, the complete tree of stock prices for a specified
number of time periods can be determined as shown Fig. 22.5.
For any time period i, i + 1 stock prices will be available at the end of the
tree.
The current price of the option is taken as the discounted weighted average of
possible future option values. There are several nodes in the diagram.
Calculations start at the final nodes of the tree and move backwards to the
start of the tree. The process can be illustrated through an example.
Example 4 The current market price of a stock is ` 150. The stock has a
volatility of 40 per cent. The risk free interest rate is 10 per cent p.a. Using
the binomial tree with monthly intervals, calculate:
(a) The 3 possible prices for the stock after 2 periods.
(b) The value of a European call option on the stock with an exercise price of
` 160.
(a) The binomial tree of stock prices for two time intervals is shown in Fig.
22.6.
(b) Calculation of the value of European call option with exercise price of `
160.
Step 1: The value of a call option on expiry is:
Max [(ST − K), 0]
The option values at the final nodes (D, E and F) are determined as:
D = Max [(188.97 − 160.00), 0] = 28.97
E = Max [(150 − 160),0] = 0
F = Max [(119.06 − 160),0] = 0
Step 2: The option values at preceding nodes (B and C) are calculated from
the option values at the final nodes.
The option value at node B is taken as the present value of the expected
option value of the possible option values at nodes D and E.
Expected option value of possible option values at D and E.
= (28.97 × 0.5076) + (0 × 0.4924) = 14.71
Present value of the expected option value
= 14.71 e−rt = 14.71 e−(0.10) (1/12)
= 14.71 (0.9917) = 14.59
The option value at node C is taken as the present value of the expected
option value of the possible option values at nodes E and F.
Since the possible option values at nodes E and F are both 0, option value at
node C is taken as 0.
Step 3: Now the option value at the initial node A can be calculated from the
option values at nodes B and C.
Expected option value of possible option values at nodes B and C
= (14.59 × 0.5076) + (0 × 0.4924)
= 7.41
Present value of the expected option value
= 7.41 e−rt = 7.41 e−(0.10)(1/12)
= 7.41 (0.9917) = 7.35
This is the estimate for the option’s current value.
The option values at the different nodes may be shown along with the
possible stock prices in the bnomial tree. This is presented in Fig. 22.7.
This analysis may be extended to more time intervals. The number of nodes
will increase and the iterative process of option value calculation will involve
more steps.
Example 5 Using the data of Example 4, calculate:
(a) The 4 possible prices for the stock after 3 periods.
(b) The value of a European call option in the stock with an exercise price of
` 160.
Solution The values of u, d and p have been calculated.
u = 1.1224
d = 0.8909
p = 0.5076
(1 − p) = 0.4924
(a) The binomial tree of stock prices forthree time intervals is shown in Fig.
22.8.
(b) Calculation of the value of European call option
Step 1: The option values at the final nodes (G, H, I and J) are:
G = Max [(212.10 − 160), 0] = 52.10
H = Max [(168.36 − 160), 0] = 8.36
I = Max [(133.64 − 160), 0] = 0
J = Max [(106.07 − 160), 0] = 0
Step 2: The option values at the preceding nodes (D, E and F):
Option value at node D:
Expected option value of possible option values at G and H
= (52.10 × 0.5076) + (8.36 × 0.4924) = 30.56
Present value of the expected option value
= 30.56 e−rt = 30.56 e−(0.10) (1/12)
= 30.56 (0.9917) = 30.31
Option value at node E:
Expected option value of possible option values at H and I
= (8.36 × 0.5076) + (0 × 0.4924) = 4.24
Present value of the expected option value
= 4.24 e−rt = 4.24 (0.9917) = 4.20
Option value at node F:
Since the option values at nodes I and J are both 0, the option value at node F
is taken as 0.
Step 3: The option values at the preceding nodes (B and C):
Option value at node B:
Expected option value of possible option values at D and E
= (30.31 × 0.5076) + (4.20 × 0.4924) = 17.45
Present value of the expected option value
= 17.45 e−rt = 17.45 (0.9917) = 17.31
Option value at node C:
Expected option value of possible option values at E and F
= (4.20 × 0.5076) + (0 × 0.4924) = 2.13
Present value of the expected option value
= 2.13 e−rt = 2.13 (0.9917) = 2.11
Step 4: The option value at the initial node A:
Expected option value of possible option values at B and C
= (17.31 × 0.5076) + (2.11 × 0.4924) = 9.83
Present value of the expected option value
= 9.83 e−rt = 9.83 (0.9917) = 9.75
The estimate for the option’s current value is ` 9.75.
The option values at different nodes along with the possible stock prices are
given in Fig. 22.9.
The Case of the American Option
The European option can be exercised only on maturity, whereas an
American option can be exercised at any time prior to expiry. Hence, an
American option may be exercised early to take advantage of a favourable
situation. While using the Binomial tree for finding the value of an American
option, the possibility of early exercise of the option has to be taken into
account. In the backwards induction process, the consequence of early
exercise is explicitly considered in case of an American option. At each
intervening node, i.e. the nodes other than the initial and final nodes, the
option value from early exercise is compared with the option value from
waiting till maturity. The higher of the two values is taken as the option value
at that node. The process is illustrated in the example given below.
Example 6 Using the date of Example 22.4, calculate:
(a) the 4 possible prices for the stock after 3 periods.
(b) the value of an American call option on the stock with an exercise price
of ` 160.
Solution The values of u, d and p have been calculated.
u = 1.1224
d = 0.8909
p = 0.5076
(1 − p) = 0.4924
(a) Binomial tree of stock prices for 3 time intervals
(b) Calculation of the value of American call option
Step 1: The option values at the final nodes
G = 52.10
H = 8.36
I=0
J=0
Step 2: The option values at the preceding nodes (D, E and F)
Option value at D:
Option value from waiting till maturity
(Already calculated in example 13.5) = 30.31
Option value from early exercise
= Max. [(ST − K), 0] = Max. [(188.97 − 160),0] = 28.97
The higher of the two values (namely, 30.31) is taken as the option value at D
Option value at E:
Option value from waiting till maturity = 4.20
Option value from early exercise
= Max. [(150 − 160), 0] = 0
The higher of the two values (4.20) is taken as the option value at E
Option value at F:
Since the stock price at F is less than the exercise price, there is no value
from early exercise. The option value from waiting till maturity is also 0.
Step 3: The option values at the preceding nodes (B and C)
Option value at B:
Option value from waiting = 17.31
Option value from early exercise
= Max. [(168.36 − 160), 0] = 8.36
The higher value (17.31) is taken as the option value.
Option value at C:
Option value from waiting = 2.11
Option value from early exercise
= Max. [(133.64 − 160), 0] = 0
The higher of the two values (2.11) is taken as the option value.
Step 4: The option value at the initial node A
Since there is no change in the option values at nodes B and C, the already
calculated value (Example 13.5) of ` 9.75 is valid.
In this illustration, early exercise does not provide a higher value at any of the
intervening nodes. Hence, there is no favourable opportunity for early
exercise. This American option would be exercised only at maturity, similar
to a European option. Hence, its current value is equal to the current value of
a European option.
Now we shall consider the case of an American put option.
Example 7 A three month American put option on a non-dividend paying
stock has an exercise price of ` 490. The current stock price is ` 500. The risk
free interest rate is 5 per cent per annum and the stock volatility is 30 per
cent. Use a binomial tree with a time step of 1 month to calculate the option
price.
Solution
Given:
S0 = ` 500
K = ` 490
r = 0.05
σ = 0.30
t = 1/12 or 0.0833
The binomial tree of stock prices for 3 time intervals can be drawn.
Calculation of option values at different nodes can be done in 4 steps.
Step 1: Option values at final nodes (G, H, I, J)
Value of a put option on expiry is:
Max [(K − ST), 0]
G = Max [(490 − 648.41), 0] = 0
H = Max [(490 − 545.25), 0] = 0
I = Max [(490 − 458.50), 0] = 31.50
J = Max [(490 − 385.54), 0] = 104.46
Step 2: Option values at preceding nodes (D, E, F)
Option value at D:
Option value from early exercise
= Max [(490 − 594.60), 0] = 0
Option value from waiting till maturity
Expected option value of possible option values at nodes G and H
Since both these values are 0, option value is taken as 0.
Option value at E:
Option value from early exercise
= Max [(490 − 500), 0] = 0
Option value from waiting till maturity
Expected option value of possible option values at nodes H and I
= (0 × 0.5026) + (31.50 × 0.4974) = 15.67
Present value of the expected option value
= 15.67 e−rt = 15.67 e−(0.05)(0.0833)
= 15.67 (0.9959) = 15.61
The option value is taken as 15.61
Option value at F:
Option value from early exercise
= Max [(490 − 420.44), 0] = 69.56
Option value from waiting till maturity
Expected option value of possible option values at nodes I and J
= (31.50 × 0.5026) + (104.46 × 0.4974) = 67.79
Present value = 67.79 e−rt = 67.79 (0.9959) = 67.51
The higher of the two values (69.56) is taken as the option value.
Step 3: Option values at preceding nodes (B and C)
Option value at B:
Option value from early exercise
= Max [(490 − 545.25), 0] = 0
Option value from waiting
Expected option value of possible option values at nodes D and E
= (0 × 0.5026) + (15.61 × 0.4974) = 7.76
Present value = 7.76 e−rt = 7.76 (0.9959) = 7.73
Option value is taken as 7.73
Option value at C:
Option value from early exercise
= Max [(490 − 458.50), 0] = 31.50
Option value from waiting
Expected option value of possible option values at nodes E and F
= (15.61 × 0.5026) + (69.56 × 0.4974) = 42.44
Present value = 42.44 e−rt = 42.44 (0.9959) = 42.27
The higher of the two values (42.27) is taken as the option value
Step 4: Option value at initial node A
Expected option value of possible option values at nodes B and C
= (7.73 × 0.5026) + (42.27 ×0.4974) = 24.91
Present value = 24.91 e−rt = 24.91 (0.9959) = 24.81
The option value at the initial node is taken as the current value of the option.
This is ` 24.81.
THE BLACK-SCHOLES MODEL AND THE BINOMIAL
MODEL— A CONTRAST
The first major advance in option pricing was made by Black and Scholes in
1973 through the development of a mathematical model for pricing stock
options. The next was made by Cox, Ross and Rubinstein in 1979, in the
form of the Binomial model for stock option pricing.
The Black-Scholes model is the most commonly used option pricing model.
The model is popular because it provides an analytical solution through a
formula. The formula can be programmed into a computer or calculator to
obtain option prices quickly. The model was developed for valuing European
style options. Hence, it may not provide reliable results when used for
valuing American style options where early exercise of the option is a
possibility.
The Binomial model can be used successfully for valuing American style
options which may be exercised early (that is, before maturity). The Binomial
model is more flexible, allowing for variations in interest rates and stock
volatility during the life of the option. A major disadvantage of the Binomial
model is that it does not permit an analytical solution through a formula; the
solution has to be obtained numerically through an iterative process involving
several steps.
EXERCISES
1. The current market price of HDFC is ` 704. The volatility of the share is
measured as 74 per cent. The interest rate on Govt. securities is 6.25 per
cent p.a. There is a call option as well as a put option, expiring in 8
months, with exercise price of ` 700. Calculate the price of the call
option and the put option using Black-Scholes model.
2. The call option on Hindustan Unilever, with exercise price of ` 340 and
expiring after 2 months, is priced at ` 15.20. The current market price of
the share is ` 327.50. The interest rate on Govt. securities is 8.25 per cent
p.a. Calculate the price of the put option on Hindustan Unilever with the
same strike price and expiry.
3. The stock underlying a European call option is expected to pay two
interim dividends of ` 15 and ` 18 after 2 months and 8 months from
now, respectively. The interest rate on Govt. securities is 9.10 per cent
p.a. Calculate the present value of the dividends.
4. Call option on Reliance Industries, expiring after 3 months from now,
has exercise price of ` 900. The current market price of the share is `
870. An interim dividend of ` 8 per share is expected from the company
after 5 months. The variance of share prices is measured as 132 per cent.
The risk free interest rate is 6.75 per cent p.a. Calculate the call option
price, using Black-Scholes pricing formula. What would be the price of
a put option with same expiry and exercise price?
5. The current market price of Federal Bank is ` 443. The stock volatility
measured by variance of stock prices is 156 per cent. The risk free rate
of return is 7.40 per cent p.a. Use the binomial tree with monthly
intervals to calculate:
(a) Possible stock prices after two intervals
(b) The value of a European call option on the stock with an exercise
price of ` 450.
6. The current market price of Titan Industries is ` 214. The stock has a
volatility of 56 per cent. The interest rate on Govt. securities is 8.10 per
cent p.a. Use the binomial tree with bi-monthly intervals to calculate:
(a) Possible stock prices after 3 intervals
(b) The value of a European call option on the stock with an exercise
price of ` 225.
7. The current market price of Ranbaxy Laboratories is ` 537. A put option
on the stock has an exercise price of ` 525. The risk free interest rate is
6.15 per cent p.a. The stock volatility, measured by variance of stock
prices, is 84 per cent. Use a binomial tree with monthly intervals to
calculate:
(a) Possible stock prices after 3 time intervals
(b) The value of the European put option on the stock.
8. An American call option on Exide Industries has an exercise price of `
150. The current market price of the stock is ` 142. The stock volatility
is 60 per cent and the risk free interest rate is 7.65 per cent p.a. Use a
binomial tree with bi-monthly intervals to calculate:
(a) Possible stock prices after 3 time intervals
(b) The value of the American call option.
REVIEW QUESTIONS
1. What is an option?
2. What are the factors affecting option prices according to Black-Scholes
model?
3. Explain the impact of the following variables on option value:
(a) Current stock price
(b) Time to expiration
(c) Volatility of the stock price
4. List the assumptions of the Black-Scholes option pricing model.
5. Explain the Black-Scholes option pricing formula for
(a) Call option
(b) Put option
6. What is Put-call parity? How is it used in calculating the put option
price?
7. Explain how dividends anticipated during the life of an option are
incorporated in the Black-Scholes option pricing formula.
8. Write a note on pricing of American options under the Black-Scholes
option pricing model.
9. Explain and illustrate the binomial tree of future stock prices.
10. “Under the binomial option pricing model, the current option price is
taken as the discounted weighted average of possible future option
values.” Explain.
11. Explain the importance of u, d and p in the binomial model.
12. Illustrate how the values of u, d and p are calculated.
13. How is an American option valued under the binomial model?
14. Compare and contrast the Black-Scholes model with the Binomial
model.
MATHEMATICAL TABLES
TABLE 1: THE NATURAL LOGARITHM (BASE e)
x
ln x
x
ln x
X
ln x
X
ln x
0.5
−0.69315
1
0
1.5
0.40547
0.01
−4.60517
0.51
0.67334
1.01
0.00995
1.6
0.47000
0.02
−3.91202
0.52
0.65393
1.02
0.0198
1.7
0.53063
0.03
0.50656
0.53
0.63488
1.03
0.02956
1.8
0.58779
0.04
0.21888
0.54
0.61619
1.04
0.03922
1.9
0.64185
0.05
−2.99573
0.55
0.59784
1.05
0.04879
2
0.69315
0.06
0.81341
0.56
0.57982
1.06
0.05827
2.1
0.74194
0.07
0.65926
0.57
0.56212
1.07
0.06766
2.2
0.78846
0.08
0.52573
0.58
0.54473
1.08
0.07696
2.3
0.83291
0.09
0.40795
0.59
0.52763
1.09
0.08618
2.4
0.87547
0.1
−2.30259
0.6
−0.51083
1.1
0.09531
2.5
0.91629
0.11
0.20727
0.61
0.4943
1.11
0.10436
2.6
0.95551
0.12
0.12026
0.62
0.47804
1.12
0.11333
2.7
0.99325
0.13
0.04022
0.63
0.46024
1.13
0.12222
2.8
1.02962
0.14
−1.96611
0.64
0.44629
1.14
0.13103
2.9
1.06471
0.15
0.89712
0.65
0.43708
1.15
0.13976
3
1.09861
0.16
0.83258
0.66
0.41552
1.16
0.14842
4
1.38629
0.17
0.77196
0.67
0.40048
1.17
0.157
5
1.60944
0.18
0.7148
0.68
0.38566
1.18
0.16551
10
2.30258
0.19
0.66073
0.69
0.37106
1.19
0.17395
0.2
−1.60944
0.7
−0.35667
1.2
0.18232
0.21
0.56065
0.71
0.34249
1.21
0.19062
0.22
0.51413
0.72
0.3285
1.22
0.19885
0.23
0.46968
0.73
0.31471
1.23
0.20701
0.24
0.42712
0.74
0.30111
1.24
0.21511
0.25
0.38629
0.75
0.28768
1.25
0.22314
0.26
0.34707
0.76
0.27444
1.26
0.23111
0.27
0.30933
0.77
0.26136
1.27
0.23902
0.28
0.27297
0.78
0.24846
1.28
0.24686
0.29
0.23787
0.79
0.23572
1.29
0.25464
0.3
−1.20397
0.8
−0.22314
1.3
0.26236
0.31
0.17118
0.81
0.21072
1.31
0.27003
0.32
0.13943
0.82
0.19845
1.32
0.27763
0.33
0.10866
0.83
0.18633
1.33
0.28518
0.34
0.07881
0.84
0.17435
1.34
0.29267
0.35
−1.04982
0.85
−0.16252
1.35
0.2001
0.36
0.02165
0.86
0.15032
1.36
0.30748
0.37
−0.99425
0.87
0.13926
1.37
0.31481
0.38
0.96758
0.88
0.12783
1.38
0.32208
0.39
0.94161
0.89
0.11653
1.39
0.3293
0.4
−0.91629
0.9
−0.10536
1.4
0.33647
0.41
0.8916
0.91
0.09431
1.41
0.34359
0.42
0.8675
0.92
0.08338
1.42
0.35066
0.43
0.84397
0.93
0.07257
1.43
0.35767
0.44
0.82098
0.94
0.06188
1.44
0.36464
0.45
0.79851
0.95
0.05129
1.45
0.37156
0.46
0.77653
0.96
0.04082
1.46
0.37844
0.47
0.75502
0.97
0.03046
1.47
0.38526
0.48
0.73397
0.98
0.0202
1.48
0.39204
0.49
0.71335
0.99
0.01005
1.49
0.39878
Source: David A. Dubofsky, Options and Financial Futures: Valuation and Uses, New York: McGraw-Hill, Inc.,
1992, p. 216.
Examples: ln (0.04) = −3.21888: ln (0.77) = −0.26136; ln (1.15) = 0.13976
TABLE 2: POWERS OF e
x
−x
X
e
−x
X
e
1
1
0.5
1.6487
0.60653
1
2.7183
0.36788
0.01
1.0101
0.99005
0.51
1.6653
0.6005
1.2
3.3201
0.30119
0.02
1.0202
0.9802
0.52
1.682
0.59452
1.3
3.6693
0.27253
0.03
1.0305
0.97045
0.53
1.6989
0.5886
1.4
4.0552
0.2466
0.04
1.0408
0.96079
0.54
1.716
0.58275
1.5
4.4817
0.22313
0.05
1.0513
0.95132
0.55
1.7333
0.57695
1.6
4.953
0.2019
0.06
1.0618
0.94176
0.56
1.7507
0.57121
1.7
5.4739
0.18268
0.07
1.0725
0.93239
0.57
1.7683
0.56553
1.8
6.0496
0.1653
0.08
1.0833
0.92312
0.58
1.786
0.5599
1.9
6.6859
0.14957
0.09
1.0942
0.91393
0.59
1.804
0.55433
2
7.3891
0.13534
0.1
1.1052
0.90484
0.6
1.8221
0.54881
3
20.086
0.04979
0.11
1.1163
0.89583
0.61
1.8404
0.54335
4
54.598
0.01832
0.12
1.1275
0.88692
0.62
1.8589
0.53794
5
148.41
0.00674
0.13
1.1388
0.87809
0.63
1.8776
0.53259
6
403.43
0.00248
0.14
1.1503
0.86936
0.64
1.8965
0.52729
7
1096.6
0.00091
0.15
1.1618
0.96071
0.65
1.9155
0.52205
8
2981
0.00034
0.16
1.1735
0.85214
0.66
1.9348
0.51685
9
8103.1
0.00012
0.17
1.1853
0.84366
0.67
1.9542
0.51171
10
22026.5
0.00005
0.18
1.1972
0.83527
0.68
1.9739
0.50662
0.19
1.2092
0.82696
0.69
1.9937
0.50158
0.2
1.2214
0.81873
0.7
2.0138
0.49659
0.21
1.2337
0.81058
0.71
2.034
0.49164
0.22
1.2461
0.80252
0.72
2.0544
0.48675
0.23
1.2586
0.79432
0.73
2.0751
0.48191
0.24
1.2712
0.78663
0.74
2.0959
0.47711
0.25
1.284
0.7788
0.75
2.117
0.47237
x
e
0
e
x
e
x
−x
e
0.26
1.2969
0.77105
0.76
2.1383
0.46767
0.27
1.31
0.76338
0.77
2.1598
0.46301
0.28
1.3231
0.75578
0.78
2.1815
0.45841
0.29
1.3364
0.74826
0.79
2.2034
0.45384
0.3
1.3499
0.74082
0.8
2.2255
0.44933
0.31
1.3634
0.73345
0.81
2.2479
0.44486
0.32
1.3771
0.72615
0.82
2.2705
0.44043
0.33
1.391
0.71892
0.83
2.2933
0.43605
0.34
1.4049
0.71177
0.84
2.3164
0.43171
0.35
1.4191
0.70469
0.85
2.3396
0.42741
0.36
1.4333
0.69768
0.86
2.3632
0.42316
0.37
1.4477
0.69073
0.87
2.3869
0.41895
0.38
1.4623
0.68386
0.88
2.4109
0.41478
0.39
1.477
0.67706
0.89
2.4351
0.41066
0.4
1.4918
0.67032
0.9
2.4596
0.40657
0.41
1.5068
0.66365
0.91
2.4843
0.40252
0.42
1.522
0.65705
0.92
2.5093
0.39852
0.43
1.5373
0.65051
0.93
2.5345
0.39455
0.44
1.5527
0.64404
0.94
2.56
0.39063
0.45
1.5683
0.63763
0.95
2.5857
0.38674
0.46
1.5841
0.63128
0.96
2.6117
0.38298
0.47
1.6
0.625
0.97
2.6379
0.37908
0.48
1.6161
0.61878
0.98
2.6645
0.37531
0.49
1.6323
0.61263
0.99
2.6912
0.37158
Source: David A. Dubofsky, Options and Financial Futures: Valuation and Uses, New York: McGraw-Hill, Inc.,
1992, p. 217.
TABLE 3: CUMULATIVE NORMAL DISTRIBUTION
This table shows values of N(x) for x < 0. The table should be used with
interpolation.
For example,
N(−0.1234) = N(−0.12) − 0.34[N(−0.12) − N(−013)]
= 0.4522 − 0.34 × (0.4522 − 0.4483) = 0.4509
x
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0
0.5
0.496
0.492
0.488
0.484
0.4801
0.4761
0.4721
0.4681
0.4641
−0.1
0.4602
0.4562
0.4522
0.4483
0.4443
0.4404
0.4364
0.4325
0.4286
0.4247
−0.2
0.4207
0.4168
0.4129
0.409
0.4052
0.4013
0.3974
0.3936
0.3897
0.3859
−0.3
0.3821
0.3783
0.3745
0.3707
0.3669
0.3632
0.3594
0.3557
0.352
0.3483
−0.4
0.3446
0.3409
0.3372
0.3336
0.33
0.3264
0.3228
0.3192
0.3156
0.3121
−0.5
0.3085
0.305
0.3015
0.2981
0.2946
0.2912
0.2877
0.2843
0.281
0.2776
−0.6
0.2743
0.2709
0.2676
0.2643
0.2611
0.2578
0.2546
0.2514
0.2483
0.2451
−0.7
0.242
0.2389
0.2358
0.2327
0.2296
0.2266
0.2236
0.2206
0.2177
0.2148
−0.8
0.2119
0.209
0.2061
0.2033
0.2005
0.1977
0.1949
0.1922
0.1894
0.1867
−0.9
0.1841
0.1814
0.1788
0.1762
0.1736
0.1711
0.1685
0.166
0.1635
0.1611
−1
0.1587
0.1562
0.1539
0.1515
0.1492
0.1469
0.1446
0.1423
0.1401
0.1379
−1.1
0.1357
0.1335
0.1314
0.1292
0.1271
0.1251
0.123
0.121
0.119
0.117
−1.2
0.1151
0.1131
0.1112
0.1093
0.1075
0.1056
0.1038
0.102
0.1003
0.0985
−1.3
0.0968
0.0951
0.0934
0.0918
0.0901
0.0885
0.0869
0.0853
0.0838
0.0823
−1.4
0.0808
0.0793
0.0778
0.0764
0.0749
0.0735
0.0721
0.0708
0.0694
0.0681
−1.5
0.0668
0.0655
0.0643
0.063
0.0618
0.0606
0.0594
0.0582
0.0571
0.0559
−1.6
0.0548
0.0537
0.0526
0.0516
0.0505
0.0495
0.0485
0.0475
0.0465
0.0455
−1.7
0.0446
0.0436
0.0427
0.0418
0.0409
0.0401
0.0392
0.0384
0.0375
0.0367
−1.8
0.0359
0.0351
0.0344
0.0336
0.0329
0.0322
0.0314
0.0307
0.0301
0.0294
−1.9
0.0287
0.0281
0.0274
0.0268
0.0262
0.0256
0.025
0.0244
0.0239
0.0233
−2
0.0228
0.0222
0.0217
0.0212
0.0207
0.0202
0.0197
0.0192
0.0188
0.0183
−2.1
0.0179
0.0174
0.017
0.0166
0.0162
0.0158
0.0154
0.015
0.0146
0.0143
−2.2
0.0139
0.0136
0.0132
0.0129
0.0125
0.0122
0.0119
0.0116
0.0113
0.011
−2.3
0.0107
0.0104
0.0102
0.0099
0.0096
0.0094
0.0091
0.0089
0.0087
0.0084
−2.4
0.0082
0.008
0.0078
0.0075
0.0073
0.0071
0.0069
0.0068
0.0066
0.0064
−2.5
0.0062
0.006
0.0059
0.0057
0.0055
0.0054
0.0052
0.0051
0.0049
0.0048
−2.6
0.0047
0.0045
0.0044
0.0043
0.0041
0.004
0.0039
0.0038
0.0037
0.0036
−2.7
0.0035
0.0034
0.0033
0.0032
0.0031
0.003
0.0029
0.0028
0.0027
0.0026
−2.8
0.0026
0.0025
0.0024
0.0023
0.0023
0.0022
0.0021
0.0021
0.002
0.0019
−2.9
0.0019
0.0018
0.0018
0.0017
0.0016
0.0016
0.0015
0.0015
0.0014
0.0014
−3
0.0014
0.0013
0.0013
0.0012
0.0012
0.0011
0.0011
0.0011
0.001
0.001
−3.1
0.001
0.0009
0.0009
0.0009
0.0008
0.0008
0.0008
0.0008
0.0007
0.0007
−3.2
0.0007
0.0007
0.0006
0.0006
0.0006
0.0006
0.0006
0.0005
0.0005
0.0005
−3.3
0.0005
0.0005
0.0005
0.0004
0.0004
0.0004
0.0004
0.0004
0.0004
0.0003
−3.4
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0.0002
−3.5
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
−3.6
0.0002
0.0002
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
−3.7
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
−3.8
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
−3.9
0
0
0
0
0
0
0
0
0
0
-4
0
0
0
0
0
0
0
0
0
0
th
Source: John C. Hull, Fundamentals of Futures and Options Markets, 4 ed., Delhi: Pearson Education, 2003, p.
477.
TABLE 4: CUMULATIVE NORMAL DISTRIBUTION
This table shows values of N(x) for x > 0. The table should be used with
interpolation.
For example,
N(0.6278) = N(0.62) + 0.78[N(0.63) − N(0.62)]
= 0.7324 + 0.78 × (0.7357 − 0.7324) = 0.7350
x
.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.5
0.504
0.508
0.512
0.516
0.5199
0.5239
0.5279
0.5319
0.5359
0.1
0.5398
0.5438
0.5478
0.5517
0.5557
0.5596
0.5636
0.5675
0.5714
0.5753
0.2
0.5793
0.5832
0.5871
0.591
0.5948
0.5987
0.6026
0.6064
0.6103
0.6141
0.3
0.6179
0.6217
0.6255
0.6293
0.6331
0.6368
0.6406
0.6443
0.648
0.6517
0.4
0.6554
0.6591
0.6628
0.6664
0.67
0.6736
0.6772
0.6808
0.6844
0.6879
0.5
0.6915
0.695
0.6985
0.7019
0.7054
0.7088
0.7123
0.7157
0.719
0.7224
0.6
0.7257
0.7291
0.7324
0.7357
0.7389
0.7422
0.7454
0.7486
0.7517
0.7549
0.7
0.758
0.7611
0.7642
0.7673
0.7704
0.7734
0.7764
0.7794
0.7823
0.7852
0.8
0.7881
0.791
0.7939
0.7967
0.7995
0.8023
0.8051
0.8078
0.8106
0.8133
0.9
0.8159
0.8186
0.8212
0.8238
0.8264
0.8289
0.8315
0.834
0.8365
0.8389
1.0
0.8413
0.8438
0.8461
0.8485
0.8508
0.8531
0.8554
0.8577
0.8599
0.8621
1.1
0.8643
0.8665
0.8686
0.8708
0.8729
0.8749
0.877
0.879
0.881
0.883
1.2
0.8849
0.8869
0.8888
0.8907
0.8925
0.8944
0.8962
0.898
0.8997
0.9015
1.3
0.9032
0.9049
0.9066
0.9082
0.9099
0.9115
0.9131
0.9147
0.9162
0.9177
1.4
0.9192
0.9207
0.9222
0.9236
0.9251
0.9265
0.9279
0.9292
0.9306
0.9319
1.5
0.9332
0.9345
0.9357
0.937
0.9382
0.9394
0.9406
0.9418
0.9429
0.9441
1.6
0.9452
0.9463
0.9474
0.9484
0.9495
0.9405
0.9515
0.9525
0.9535
0.9545
1.7
0.9554
0.9564
0.9573
0.9582
0.9591
0.9599
0.9608
0.9616
0.9625
0.9633
1.8
0.9641
0.9649
0.9656
0.9664
0.9671
0.9678
0.9686
0.9693
0.9699
0.9706
1.9
0.9713
0.9719
0.9726
0.9732
0.9738
0.9744
0.975
0.9756
0.9761
0.9767
2.0
0.9772
0.9778
0.9783
0.9788
0.9793
0.9798
0.9803
0.9808
0.9812
0.9817
2.1
0.9821
0.9826
0.983
0.9834
0.9838
0.9842
0.9846
0.985
0.9854
0.9857
2.2
0.9861
0.9864
0.9868
0.9871
0.9875
0.9878
0.9881
0.9884
0.9887
0.989
2.3
0.9893
0.9896
0.9898
0.9901
0.9904
0.9906
0.9909
0.9911
0.9913
0.9916
2.4
0.9918
0.992
0.9922
0.9925
0.9927
0.9929
0.9931
0.9932
0.9934
0.9936
2.5
0.9938
0.994
0.9941
0.9943
0.9945
0.9946
0.9948
0.9949
0.9951
0.9952
2.6
0.9953
0.9955
0.9956
0.9957
0.9959
0.996
0.9961
0.9962
0.9963
0.9964
2.7
0.9965
0.9966
0.9967
0.9968
0.9969
0.997
0.9971
0.9972
0.9973
0.9974
2.8
0.9974
0.9975
0.9976
0.9977
0.9977
0.9978
0.9979
0.9979
0.998
0.9981
2.9
0.9981
0.9982
0.9982
0.9983
0.9984
0.9984
0.9985
0.9985
0.9986
0.9986
3.0
0.9986
0.9987
0.9987
0.9988
0.9988
0.9989
0.9989
0.9989
0.999
0.999
3.1
0.999
0.9991
0.9991
0.9991
0.9992
0.9992
0.9992
0.9992
0.9993
0.9993
3.2
0.9993
0.9993
0.9994
0.9994
0.9994
0.9994
0.9994
0.9995
0.9995
0.9995
3.3
0.9995
0.9995
0.9995
0.9996
0.9996
0.9996
0.9996
0.9996
0.9996
0.9997
3.4
0.9997
0.9997
0.9997
0.9997
0.9997
0.9997
0.9997
0.9997
0.9997
0.9998
3.5
0.9998
0.9998
0.9998
0.9998
0.9998
0.9998
0.9998
0.9998
0.9998
0.9998
3.6
0.9998
0.9998
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
3.7
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
3.8
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
0.9999
3.9
1
1
1
1
1
1
1
1
1
1
4.0
1
1
1
1
1
1
1
1
1
1
th
Source: John C. Hull, Fundamentals of Futures and Options Markets, 4 ed., Delhi: Pearson Education, 2003, p.
478.
APPENDIX
Table A1 Present Value Factors (PVFs) for Pairs of r (%) and n (periods)
n
r
1
2
3
4
5
6
7
8
9
10
11
12
0.25 0.9975 0.9950 0.9925 0.9901 0.9876 0.9851 0.9827 0.0802 0.9778 0.9753 0.9729 0.9705 0.9681
0.50 0.9950 0.9901 0.9851 0.9802 0.9754 0.9705 0.9657 0.9609 0.9561 0.9513 0.9466 0.9419 0.9372
0.75 0.9926 0.9852 0.9778 0.9706 0.9633 0.9562 0.9490 0.9420 0.9350 0.9280 0.9211 0.9142 0.9074
1
0.9901 0.9803 0.9706 0.9610 0.9515 0.9420 0.9327 0.9235 0.9143 0.9053 0.8963 0.8874 0.8787
2
0.9804 0.9612 0.9423 0.9238 0.9057 0.8880 0.8706 0.8535 0.8368 0.8203 0.8043 0.7885 0.7730
3
0.9709 0.9426 0.9151 0.8885 0.8626 0.8375 0.8131 0.7894 0.7664 0.7441 0.7224 0.7014 0.6810
4
0.9615 0.9246 0.8890 0.8548 0.8219 0.7903 0.7599 0.7307 0.7026 0.6756 0.6496 0.6246 0.6006
5
0.9524 0.9070 0.8638 0.8227 0.7835 0.7462 0.7107 0.6768 0.6446 0.6139 0.5847 0.5568 0.5303
6
0.9434 0.8900 0.8396 0.7921 0.7473 0.7050 0.6651 0.6274 0.5919 0.5584 0.5268 0.4970 0.4688
7
0.9346 0.8734 0.8163 0.7629 0.7130 0.6663 0.6227 0.5820 0.5439 0.5083 0.4751 0.4440 0.4150
8
0.9259 0.8573 0.7938 0.7350 0.6806 0.6302 0.5835 0.5403 0.5002 0.4632 0.4289 0.3971 0.3677
9
0.9174 0.8417 0.7722 0.7084 0.6499 0.5963 0.5470 0.5019 0.4604 0.4224 0.3875 0.3555 0.3262
10
0.9091 0.8264 0.7513 0.6830 0.6209 0.5645 0.5132 0.4665 0.4241 0.3855 0.3505 0.3186 0.2897
11
0.9009 0.8116 0.7312 0.6587 0.5935 0.5346 0.4817 0.4339 0.3909 0.3522 0.3173 0.2858 0.2575
12
0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039 0.3606 0.3220 0.2875 0.2567 0.2292
13
0.8850 0.7831 0.6931 0.6133 0.5428 0.4803 0.4251 0.3762 0.3329 0.2946 0.2607 0.2307 0.2042
14
0.8772 0.7695 0.6750 0.5921 0.5194 0.4556 0.3996 0.3506 0.3075 0.2697 0.2366 0.2076 0.1821
15
0.8696 0.7561 0.6575 0.5718 0.4972 0.4323 0.3759 0.3269 0.2843 0.2472 0.2149 0.1869 0.1625
16
0.8621 0.7432 0.6407 0.5523 0.4761 0.4104 0.3538 0.3050 0.2630 0.2267 0.1954 0.1685 0.1452
17
0.8547 0.7305 0.6244 0.5337 0.4561 0.3898 0.3332 0.2848 0.2434 0.2080 0.1778 0.1520 0.1299
18
0.8475 0.7182 0.6086 0.5158 0.4371 0.3704 0.3139 0.2660 0.2255 0.1911 0.1619 0.1372 0.1163
19
0.8403 0.7062 0.5934 0.4987 0.4190 0.3521 0.2959 0.2487 0.2090 0.1756 0.1476 0.1240 0.1042
20
0.8333 0.6944 0.5787 0.4823 0.4019 0.3349 0.2791 0.2326 0.1938 0.1615 0.1346 0.1122 0.0935
21
0.8264 0.6830 0.5645 0.4665 0.3855 0.3186 0.2633 0.2176 0.1799 0.1486 0.1228 0.1015 0.0839
22
0.8197 0.6719 0.5507 0.4514 0.3700 0.3033 0.2486 0.2038 0.1670 0.1369 0.1122 0.0920 0.0754
23
0.8130 0.6610 0.5374 0.4369 0.3552 0.2888 0.2348 0.1909 0.1552 0.1262 0.1026 0.0834 0.0678
24
0.8065 0.6504 0.5245 0.4230 0.3411 0.2751 0.2218 0.1789 0.1443 0.1164 0.0938 0.0757 0.0610
25
0.8000 0.6400 0.5120 0.4096 0.3277 0.2621 0.2097 0.1678 0.1342 0.1074 0.0859 0.0687 0.0550
26
0.7937 0.6299 0.4999 0.3968 0.3149 0.2499 0.1983 0.1574 0.1249 0.0992 0.0787 0.0625 0.0496
28
0.7813 0.6104 0.4768 0.3725 0.2910 0.2274 0.1776 0.1388 0.1084 0.0847 0.0662 0.0517 0.0404
30
0.7692 0.5917 0.4552 0.3501 0.2693 0.2072 0.1594 0.1226 0.0943 0.0725 0.0558 0.0429 0.0330
35
0.7407 0.5487 0.4064 0.3011 0.2230 0.1652 0.1224 0.0906 0.0671 0.0497 0.0368 0.0273 0.0202
40
0.7143 0.5102 0.3644 0.2603 0.1859 0.1328 0.0949 0.0678 0.0484 0.0346 0.0247 0.0176 0.0126
45
0.6897 0.4756 0.3280 0.2262 0.1560 0.1076 0.0742 0.0512 0.0353 0.0243 0.0168 0.0116 0.0080
50
0.6667 0.4444 0.2963 0.1975 0.1317 0.0878 0.0585 0.0390 0.0260 0.0173 0.0116 0.0077 0.0051
Table A2 Present Value Factors for Annuity (PVFAs) for Pairs of r (%) and n (periods)
n
r
1
2
3
4
5
6
7
8
9
10
11
12
0.25 0.9975 1.9925 2.9851 3.9751 4.9627 5.9478 6.9305 7.9107 8.8885 9.8639 10.8368 11.8073
0.50 0.9950 1.9851 2.9702 3.9505 4.9259 5.8964 6.8621 7.8230 8.7791 9.7304 10.6770 11.6189
0.75 0.9926 1.9777 2.9556 3.9261 4.8894 5.8456 6.7946 7.7366 8.6716 9.5996 10.5207 11.4349
1
0.9901 1.9704 2.9410 3.9020 4.8534 5.7955 6.7282 7.6517 8.5660 9.4713 10.3676 11.2551
2
0.9804 1.9416 2.8839 3.8077 4.7135 5.6014 6.4720 7.3255 8.1622 8.9826
9.7868
10.5753
3
0.9709 1.9135 2.8286 3.7171 4.5797 5.4172 6.2303 7.0197 7.7861 8.5302
9.2526
9.9540
4
0.9615 1.8861 2.7751 3.6299 4.4518 5.2421 6.0021 6.7327 7.4353 8.1109
8.7605
9.3851
5
0.9524 1.8594 2.7232 3.5460 4.3295 5.0757 5.7864 6.4632 7.1078 7.7217
8.3064
8.8633
6
0.9434 1.8334 2.6730 3.4651 4.2124 4.9173 5.5824 6.2098 6.8017 7.3601
7.8869
8.3838
7
0.9346 1.8080 2.6243 3.3872 4.1002 4.7665 5.3893 5.9713 6.5152 7.0236
7.4987
7.9427
8
0.9259 1.7833 2.5771 3.3121 3.9927 4.6229 5.2064 5.7466 6.2469 6.7101
7.1390
7.5361
9
0.9174 1.7591 2.5313 3.2397 3.8897 4.4859 5.0330 5.5348 5.9952 6.4177
6.8052
7.1607
10
0.9091 1.7355 2.4869 3.1699 3.7908 4.3553 4.8684 5.3349 5.7590 6.1446
6.4951
6.8137
11
0.9009 1.7125 2.4437 3.1024 3.6959 4.2305 4.7122 5.1461 5.5370 5.8892
6.2065
6.4924
12
0.8929 1.6901 2.4018 3.0373 3.6048 4.1114 4.5638 4.9676 5.3282 5.6502
5.9377
6.1944
13
0.8850 1.6681 2.3612 2.9745 3.5172 3.9975 4.4226 4.7988 5.1317 5.4262
5.6869
5.9176
14
0.8772 1.6467 2.3216 2.9137 3.4331 3.8887 4.2883 4.6389 4.9464 5.2161
5.4527
5.6603
15
0.8696 1.6257 2.2832 2.8550 3.3522 3.7845 4.1604 4.4873 4.7716 5.0188
5.2337
5.4206
16
0.8621 1.6052 2.2459 2.7982 3.2743 3.6847 4.0386 4.3436 4.6065 4.8332
5.0286
5.1971
17
0.8547 1.5852 2.2096 2.7432 3.1993 3.5892 3.9224 4.2072 4.4506 4.6586
4.8364
4.9884
18
0.8475 1.5656 2.1743 2.6901 3.1272 3.4976 3.8115 4.0776 4.3030 4.4941 4.6560
4.7932
19
0.8403 1.5465 2.1399 2.6386 3.0576 3.4098 3.7057 3.9544 4.1633 4.3389 4.4865
4.6105
20
0.8333 1.5278 2.1065 2.5887 2.9906 3.3255 3.6046 3.8372 4.0310 4.1925 4.3271
4.4392
21
0.8264 1.5095 2.0739 2.5404 2.9260 3.2446 3.5079 3.7256 3.9054 4.0541 4.1769
4.2784
22
0.8197 1.4915 2.0422 2.4936 2.8636 3.1669 3.4155 3.6193 3.7863 3.9232 4.0354
4.1274
23
0.8130 1.4740 2.0114 2.4483 2.8035 3.0923 3.3270 3.5179 3.6731 3.7993 3.9018
3.9852
24
0.8065 1.4568 1.9813 2.4043 2.7454 3.0205 3.2423 3.4212 3.5655 3.6819 3.7757
3.8514
25
0.8000 1.4400 1.9520 2.3616 2.6893 2.9514 3.1611 3.3289 3.4631 3.5705 3.6564
3.7251
26
0.7937 1.4235 1.9234 2.3202 2.6351 2.8850 3.0833 3.2407 3.3657 3.4648 3.5435
3.6059
28
0.7813 1.3916 1.8684 2.2410 2.5320 2.7594 2.9370 3.0758 3.1842 3.2689 3.3351
3.3868
30
0.7692 1.3609 1.8161 2.1662 2.4356 2.6427 2.8021 2.9247 3.0190 3.0915 3.1473
3.1903
35
0.7407 1.2894 1.6959 1.9969 2.2200 2.3852 2.5075 2.5982 2.6653 2.7150 2.7519
2.7792
40
0.7143 1.2245 1.5889 1.8492 2.0352 2.1680 2.2628 2.3306 2.3790 2.4136 2.4383
2.4559
45
0.6897 1.1653 1.4933 1.7195 1.8755 1.9831 2.0573 2.1085 2.1438 2.1681 2.1849
2.1965
50
0.6667 1.1111 1.4074 1.6049 1.7366 1.8244 1.8829 1.9220 1.9480 1.9653 1.9769
1.9846
GLOSSARY
American style option: is an option contract that can be exercised any time
up to and including the expiry date of the contract.
APT (Arbitrage Pricing Theory): is a mathematical model which tries to
explain security pricing behavior with a multi factor framework. It was
developed by Stephen Ross in the mid-1970s as an alternative to the single
factor CAPM. The theory proposes that a set of multiple factors is needed to
explain security returns and thereby security pricing. It is an expression of the
relation between security return and multi risk factors. The theory does not
predetermine the factor structure; the relevant factors have to be determined
empirically. The model can be used to calculate the expected return and
expected price of a security commensurate with its risk level. The model
thereby helps to identify mispriced securities, leading to arbitrage operations
which will ultimately correct the mispricing of securities in the market.
Arbitrage: is a market operation which is initiated when there is mispricing
of assets in the market. Two assets which are equivalent in all economically
relevant aspects must have the same market price. If one of the assets is either
overpriced or underpriced, arbitrage operation will be initiated by market
participants. This involves selling of overpriced assets and buying of
underpriced assets. Continuous arbitrage will restore parity between the
prices of similar assets.
Bar chart: is a price chart in which the highest price, the lowest price and the
closing price for each day are plotted on a day-to-day basis on an XY graph.
A bar is formed by joining the highest price and the lowest price of a
particular day by a vertical line. The top of the vertical line or bar represents
the highest price of the day; the bottom of the bar represents the lowest price
of the day. A small horizontal hash on the right of the bar is used to represent
the closing price of the day.
Bear: is a speculative trader who anticipates a decline in prices of securities
in the market and takes a short position with respect to securities whose
prices are expected to decline. He attempts to cover up his short position by
buying the securities at lower prices when prices decline.
Bearish market: the phase of the stock market movement cycle in which
share prices are generally seen to be declining due to pessimistic expectations
regarding the performance of the companies and the economy.
Beta: is the measure of the systematic risk of a security. It measures the
change in security returns in relation to the change in the stock market index
return. It thus measures the variability of the security relative to the
variability of the market as a whole.
Bid price: is the price at which an investor/dealer is willing to buy the
security.
Bond duration: is the holding period of a bond at which interest rate risk
disappears. An investor in bonds faces variations in his returns due to
changes in the market interest rate during his holding period. This risk,
known as interest rate risk, occurs on account of two factors—the
reinvestment of annual interest (reinvestment risk) and the capital gain or loss
on sale of bond at the end of the holding period (price risk). When the market
interest rises, there is a gain on reinvestment but a loss on sale of bond. The
converse is true when the market interest rate falls. For any bond there is a
holding period at which these two effects exactly balance each other. That
holding period is referred to as the bond duration.
Book building: is a procedure followed in the public issue of securities.
Under this process, the issue price of a security is determined by the demand
and supply for that security. Investors are given the option to indicate the
price at which they are willing to buy the security, within a specified price
band. The price of the security is fixed as the weighted average of the prices
offered by investors. It involves a process of price discovery and is an
alternative to the fixed price method of public issue.
Bull: is a speculative trader who anticipates a rise in prices of securities and
takes a long position with respect to securities whose prices are expected to
rise in the market.
Bullish market: the phase of the stock market movement cycle in which
share prices are generally seen to be rising due to optimistic expectations
regarding the performance of the companies and the economy.
Business cycle: refers to the different phases of prosperity through which an
economy passes. These phases are boom, recession, depression and recovery.
The performance of industries and companies in an economy depends on the
phase of the business cycle through which the economy is passing.
Business risk: is the variability in operating income of a company caused by
the changes in the operating conditions of the company.
Call option: is a contract that gives the holder of the option the right to buy
an underlying asset such as a share, a stock market index, a foreign currency,
etc., at a pre determined price in the future. The person holding the option
will exercise the right to buy the underlying asset if the future price
movement of the asset is favourable to him; or else he will choose not to
exercise the right.
Capital market: is the market segment where securities with maturities of
more than one year are bought and sold. Equity shares, preference shares,
debentures and bonds are the long term securities traded in the capital market.
CAPM (Capital Asset Pricing Model): expresses a simple linear
relationship between the expected return and systematic risk of a security or
portfolio. All securities are expected to yield returns commensurate with their
riskiness as measured by beta. The expected return on any security or
portfolio can be determined from the model if we know the beta of that
security or portfolio. The model also provides a framework for evaluating the
pricing of securities, that is, whether a security is underpriced, overpriced or
correctly priced. A security will be considered to be overpriced (or
unattractive) when the expected return on the security according to CAPM
formula is higher than the actual return offered by the security. On the
contrary, a security which offers higher actual return than the expected return
(according to the CAPM formula) will be considered to be underpriced (or
attractive).
Clearing house: is the agency which is entrusted with the settlement of
trades in a stock exchange. It acts as the counter party for each trade. Sellers
of securities have to deliver the securities to the clearing house and receive
cash from the clearing house; buyers of securities have to pay cash to the
clearing house and receive the securities from the clearing house.
CML (Capital Market Line): is the straight line which expresses the
relationship between the return and risk of all efficient portfolios. The
appropriate measure of risk for an efficient portfolio is assumed to be the
standard deviation of return of the portfolio. There is a linear relationship
between risk as measured by the standard deviation and the expected return
for these efficient portfolios. This relationship is graphically represented by
the Capital Market Line.
Commodity futures: is a type of futures contracts in which the underlying
asset which is agreed to be bought or sold in the future is a commodity such
as wheat, cotton, pepper, etc.
Company analysis: refers to the detailed analysis of the operations of a
company and its effect on the level, trend and stability of earnings of the
company. It focuses on the estimation of return and risk of investment in
securities of specific companies.
Constant ratio plan: is a formula plan used in passive revision strategy. The
investor constructs two portfolios; one, aggressive, consisting of equity
shares and the other, defensive, consisting of bonds and debentures. The ratio
between the investments in the two portfolios would be predetermined such
as 1:1 or 1.5:1, etc. The purpose of the plan is to keep the ratio between the
two portfolios constant by transfer of funds from one portfolio to the other as
share prices fluctuate. As share prices rise, the value of the aggressive
portfolio would also rise, necessitating transfer of funds from the aggressive
portfolio to the defensive portfolio. The opposite would happen when share
prices decline.
Constant rupee value plan: is a popular formula plan used in passive
revision strategy. The investor constructs two portfolios; one, aggressive,
consisting of equity shares and the other, defensive, consisting of bonds and
debentures. The value of the aggressive portfolio is kept constant by
transferring funds from the aggressive portfolio to the defensive portfolio
when share prices are rising. Similarly, funds are transferred from the
defensive portfolio to the aggressive portfolio when share prices are falling
and the value of the aggressive portfolio declines. The plan helps the investor
to buy shares when prices are low and sell shares when prices are high.
Coupon rate: is the nominal interest rate applicable to a debt security such as
a bond or a debenture. It is the rate at which interest is payable by the issuing
company to the bondholder and is calculated on the face value of the debt
security.
Covariance: is the statistical measure that indicates the interactive risk of a
security relative to other securities in a portfolio of securities. The covariance
between any two securities indicates the way the security returns vary in
relation to each other whenever changes occur in the market. If the returns of
the two securities move in the same direction consistently the covariance
would be positive. If the returns move in opposite directions consistently the
covariance would be negative. If the movements of the returns are
independent of each other, covariance would be close to zero.
Covered call: is a call option written (or sold) by a party who owns or is in
possession of the underlying asset. Here, the call option sold is covered by
the already owned underlying asset. If the buyer of the call option exercises
his right to buy the underlying asset, the writer of the option can deliver the
asset which he already owns, without having to buy it from the market at a
higher price.
Current yield: is the ratio of the annual interest receivable on a debt security
to its current market price.
Day order: is an order that is valid only for the trading day on which the
order is placed. If the order is not executed by the end of the day, it is treated
as cancelled.
Deep discount bond: is a special type of bond which does not specify a
coupon rate and does not pay annual interest. The return on this type of bond
is in the form of a discount on the face value of the bond offered at the time
of issue of the bond.
Default risk: refers to the possibility of unfavourable variation in returns of
bonds due to failure of the issuing company to pay interest or principal on the
stipulated dates.
Dematerialisation: is the process of converting securities held in physical
form (as certificates) to an equivalent number of securities in electronic form
and crediting the same to the demat account of the investor.
Demat account: is an account opened by investors with Depository
Participants to hold and transfer securities in electronic form. The demat
account of an investor would be credited when a security is purchased by
him; the demat account would be debited when a security held by an investor
in the demat account is transferred or sold.
Depository: is an agency that is authorized to hold securities in electronic
form in demat accounts opened by investors. A depository facilitates transfer
of securities held in electronic form by debit and credit to the demat accounts
of the investors.
Depository Participant (DP): is an organization affiliated to a depository to
perform the depository service of operating demat accounts of investors.
Each depository has several depository participants affiliated to it to enable
investors to open demat accounts for holding and transferring securities.
Differential return: is the difference between the actual return earned on a
security or portfolio and the return expected from the security or portfolio
commensurate with its risk. The expected return is calculated using the
CAPM model. Positive differential return is an indication of superior
performance. This measure of risk adjusted performance has been developed
by Michael Jensen and is also known as Jensen ratio.
Diversification: is the process of combining securities in a portfolio. The aim
of diversification is to reduce the total risk of investment without sacrificing
the return.
Dollar cost averaging: is a technique of building up a portfolio over a period
of time at low cost. The technique stipulates that the investor invest a
constant sum, such as ` 5000 or ` 10000, in a specified share or portfolio of
shares regularly at periodic intervals, such as a month, two months, a quarter,
etc., regardless of the price of the shares at the time of investment. This
periodic investment is to be continued over a fairly long period to cover a
complete cycle of share price movements. The investor will obtain his shares
at a lower average cost per share than the average price prevailing in the
market over the investment period. When a portfolio has been constructed in
this manner, the investor may switch over to one of the formula plans for its
subsequent revision.
Dow theory: is a theory regarding stock price behavior formulated by
Charles H. Dow during 1900−1902. According to the theory, the stock
market does not move on a random basis but is influenced by three distinct
movements which occur simultaneously. These movements are the primary
movement (or the long-term trend), secondary reactions (movements in the
opposite direction to the primary movement lasting for short durations), and
minor movements (the intraday fluctuations in share prices).
Economy analysis: is the study of key macro economic variables that are
expected to influence the performance of companies in the economy so as to
estimate the trend of future corporate earnings.
Efficient frontier: is the graphical representation of all the efficient
portfolios in a set of feasible portfolios. When the expected return and the
standard deviation of all portfolios considered for investment are plotted on
an XY graph, a dark shaded area will emerge in the graph representing all the
portfolios. The portfolios lying in the north west boundary of the shaded area
are more efficient than all the portfolios in the interior of the shaded area.
This boundary of the shaded area containing all the efficient portfolios in the
set is known as the efficient frontier. It will be a concave curve.
Efficient market hypothesis (EMH): is the proposition that the financial
market is efficient in pricing securities. It implies that current market prices
of securities instantaneously and fully reflect all relevant available
information. An investor cannot consistently earn abnormal returns by
undertaking fundamental or technical analysis because there would be no
‘mispricing’ of securities.
Efficient portfolio: is a portfolio which dominates other portfolios in a set of
feasible portfolios. A portfolio is said to dominate another portfolio if it has
either a lower standard deviation and the same expected return, or a higher
expected return and the same standard deviation as the other portfolio. An
investor will be interested only in the efficient portfolios in a set of feasible
portfolios.
European style option: is an option contract that can be exercised only on
the maturity date or expiry date of the option.
Exchange traded options: are options bought and sold on organized
exchanges (the Futures and Options Exchanges). These options are
standardized as to the amount and exercise price of the underlying
instrument, the nature of the underlying instrument and the available expiry
dates. The option contracts traded in exchanges would relate to discrete
blocks or quantities of the underlying instrument and would provide a limited
range of exercise prices and expiry dates.
Exercise price: is the price at which the holder of an option can exercise his
right to buy or sell the underlying asset. The holder of a call option has the
right to buy the underlying asset at the already agreed upon exercise price any
time before the expiry date. The holder of the put option similarly has the
right to sell the underlying asset at the exercise price any time before the
expiry date.
Expiry date: is the term related to futures contracts and option contracts
which are essentially contracts to be executed in the future. Expiry date refers
to the last date on or before which the contracts have to be executed. It
indicates the maturity period of the contracts.
Financial derivatives: are instruments used for hedging the risk involved in
buying, holding and selling different kinds of financial assets whose prices
fluctuate frequently. Each derivative instrument has an underlying asset such
as a share, a foreign currency, a debt security, a stock market index, etc. The
derivatives provide protection to participants in financial markets against
adverse movements in the prices of the underlying assets. The value of a
financial derivative is derived from the value of the underlying asset.
Financial futures: is a type of futures contracts in which the underlying asset
which is agreed to be bought or sold in the future is a financial asset such as
foreign currencies, stocks, bonds, stock index, etc.
Financial market: the mechanism or system through which financial assets
such as fixed deposits, insurance policies, mutual fund units, treasury bills,
commercial papers, etc. are created and transferred.
Financial risk: is the variability in returns available to equity shareholders of
a company due to financial leverage or use of debt in the capital structure of a
company. The use of debt creates fixed interest payment obligations which
may reduce the return available to equity shareholders.
Formula plans: are portfolio revision techniques or procedures wherein
adjustment to the portfolio is carried out according to certain predetermined
rules and procedures regarding when to buy or sell and how much to buy or
sell. These predetermined rules call for specified actions when there are
changes in the securities market. These rules enable the investor to
automatically sell shares when their prices are rising and buy shares when
their prices are falling. Formula plans are used as part of passive revision
strategy.
Forwards: are agreements to buy or sell an asset at a predetermined price
and at a specified future time. The terms of the contract such as the price,
delivery date, quantity and quality of the asset involved are specified at the
time of initiating the contract, but actual payment and delivery of the asset
occur later. Forwards are derivative securities used to hedge the risk arising
from fluctuations in asset prices.
Fundamental analysis: is a logical and systematic approach to estimating
the future earnings and share price of companies. It is based on the premise
that the earnings and share price of a company is determined by a number of
fundamental factors relating to the economy, industry and company.
Fundamental analysis is a detailed analysis of the fundamental factors
affecting the performance of companies. Fundamental analysis helps to
identify fundamentally strong companies whose shares are worthy to be
included in the investor’s portfolio.
Futures: is an agreement to buy or sell an underlying asset at a certain time
in the future for a pre determined price. The assets underlying futures
contracts may be financial assets such as shares, foreign currencies, bonds,
etc., or commodities such as gold, sugar, coffee, etc. Futures enable
participants to ‘lock in’ a price for their future transaction, thereby
eliminating uncertainty regarding the future price of the asset.
Gambling: is taking high risk not only for high return, but also for thrill and
excitement. Typical examples of gambling activities include horse races, card
games, lotteries, etc. The risks in gambling activities are artificial and
unnecessary.
Hedgers: are people who use the derivative instruments such as futures and
options to hedge the risk arising from adverse movements in the prices of
underlying assets which they either hold or need for use.
Hedging: is the process of eliminating or minimizing the risk arising from
price fluctuations of assets by using derivative instruments such as futures
and options.
Holding period yield (HPY): is the rate of return earned on a security or a
portfolio over the holding period. The return may include changes in the
value of the security or portfolio over the holding period plus any income
earned over the period. The total return earned during the holding period may
be expressed as a percentage of the investment in the security or portfolio.
Index futures: are futures contracts to buy or sell a specified stock market
index in the future at a specified price. It is a futures contract whose
underlying asset is any specified stock market index such as Nifty (India), S
& P 100 (USA), FTSE 100 (UK), etc.
Industry analysis: refers to an evaluation of the relative strengths and
weaknesses of particular industries with a view to assess the performance of
companies belonging to different industries.
Industry life cycle: is the concept that the life of an industry can be
segregated into different phases or stages such as the pioneering stage, the
expansion stage, the stagnation stage and the decay stage. Each stage of
growth is said to be unique having different characteristics. The profitability
and performance of companies belonging to an industry depends upon its
stage of growth.
Inefficient portfolio: is a portfolio which is dominated by other portfolios in
a set of feasible portfolios. A portfolio is said to be dominated by another
portfolio when that other portfolio has either a lower standard deviation and
the same expected return, or a higher expected return and the same standard
deviation as the first portfolio.
Initial margin: is also referred to as performance margin. It is the amount
to be deposited with the clearing house by both the parties to a futures
contract at the time of entering into the contract. The amount of initial margin
is fixed as a percentage of the base value of the futures contract; the
percentage may vary from contract to contract based on the risk involved in
the underlying asset.
Interest rate risk: is the variability in returns caused due to changes in
market interest rates. Fluctuations in market interest rates cause variations in
bond prices and share prices. It is a systematic risk that affects bonds directly
and shares indirectly.
Investment: involves employment of funds with the aim of achieving
additional income or growth in value. It is a commitment of funds in the
expectation of some positive rate of return to be realized in the future.
Expectation of return is an essential element of investment. Variability of the
actual return to be realized in future constitutes risk in investment.
Japanese candlestick: is a type of price chart in which each day’s prices (the
highest price, lowest price, opening price and closing price) are depicted as a
candlestick. The highest price and the lowest price of a day are joined by a
vertical line. The opening price and the closing price which fall between the
highest and the lowest prices would be represented by a rectangle so that the
price bar looks like a candlestick.
Jensen ratio: is the risk adjusted performance measure developed by
Michael Jensen. It measures the difference between the actual return earned
on a security or portfolio and the return expected from the security or
portfolio commensurate with its risk. The expected return is calculated using
the CAPM model. The ratio measures differential return and positive
differential return is an indication of superior performance.
Lame duck: is a bear who has made a short sale but is unable to meet his
commitment to deliver the security sold by him on account of rise in price of
the security subsequent to the short sale. He is said to be struggling like a
lame duck.
Limit order: is an order in which the investor specifies the price at which he
wants the transaction to be executed. In the case of a limit order to buy, the
investor specifies the maximum price or ceiling price that he will pay for the
security. In the case of a limit order to sell, the investor specifies the
minimum price or floor price he will accept for the sale transaction.
Line chart: is a price chart in which the closing prices or last traded prices of
shares are shown against days or different time periods in an XY graph.
When the prices are joined together, it results in a line showing the trend of
the market.
Liquidity: refers to the facility for conversion of an investment into cash
without loss of money and without loss of time. It is a feature that makes the
investment attractive to investors.
Listing: is the process of including the securities of a company in the official
list of the stock exchange for the purpose of trading. For the securities of a
company to be traded on a stock exchange, they have to be listed in that stock
exchange.
Long buy: is a speculative activity engaged in by speculators who anticipate
a rise in security prices in the near future. Here, the speculator agrees to buy
the security with the intention of selling it at a higher price when the price
rises as anticipated. The speculator is not interested in taking delivery of the
security concerned. He is said to take a long position with respect to the
security.
MACD (Moving Average Convergence and Divergence): is an oscillator
that measures the convergence and divergence between a short-term
exponential moving average and a long-term exponential moving average
which are calculated with the closing price data. A 12-day and 48-day
exponential moving averages constitute a popular combination. The
difference between the short-term EMA and the long-term EMA represents
MACD value. Positive values of MACD indicate a bullish market signalling
a buying opportunity, while negative values of MACD indicate a bearish
market signaling a selling opportunity.
Maintenance margin: refers to the minimum balance that the buyer and
seller of a futures contract is expected to maintain with the clearing house
throughout the duration of the contract. The maintenance margin amount is
lower than the initial margin amount and is usually fixed as a certain
percentage of the initial margin.
Margin: is a deposit to be made to the clearing house by the parties entering
into a futures contract.
Margin call: is the request sent by the clearing house of a Futures exchange
to the parties of a futures contract when the balance in their margin account
with the clearing house drops below the maintenance margin level. The party
concerned is required to deposit additional funds in the margin account to
raise the balance in the account to the initial margin level.
Margin trading: is buying of securities using borrowed funds. The investor
contributes only a part of the funds required for buying securities (known as
margin) and the balance amount is provided by banks or brokers as loan.
Margin system: refers to the procedure of maintaining a part of the full value
of the futures contract as deposit with the clearing house by both the parties
to a futures contract during the pendency of the contract. This system is
prescribed to ensure that the parties to the contract do not fail to fulfill their
obligations under the contract. Three types of margins are prescribed under
this system, namely, the initial margin (or performance margin), the
maintenance margin and the variation margin.
Market breadth: is the difference between the number of shares which
advanced and the number of shares which declined during a period. Each
day’s difference is added to the next day’s difference to form a continuous
cumulative index. It is useful in identifying the trend of the market.
Market index: is a basket of securities selected so as to represent the whole
stock market or a specified sector or segment of the market. The index is used
to measure the change in the prices of the basket of securities with reference
to a base period and after giving proper weights to different stocks on the
basis of their importance to the economy or sector of the economy. It helps in
understanding the level of prices and the trend of price movements in the
market.
Market order: is the order placed by the investor to buy or sell a stated
number of securities immediately at the best prevailing price in the market. In
the case of a buy order, the best price is the lowest price obtainable; in the
case of a sell order, the best price is the highest price obtainable.
Market risk: is the variation in security returns caused by the volatility of
the stock market. It is a type of systematic risk affecting several securities
simultaneously.
Marking-to-market: is the process of revaluing a futures contract on the
basis of the market price prevailing each day and adjusting the change in the
value of the contract in the margin accounts of the parties to the contract. The
decline in the value of a futures contract is debited to the margin account of
the buyer and credited to the margin account of the seller. On the contrary,
the increase in the value of a futures contract is credited to the buyer’s margin
account and debited to the seller’s margin account.
Markowitz model: is the mathematic process or programme used by Harry
Markowitz to identify the efficient portfolios in a set of feasible portfolios.
Using the expected return and risk of each security under consideration and
the covariance estimates for each pair of securities, he calculated risk and
return of all possible portfolios. For any specific value of expected portfolio
return, the least risk portfolio is identified using quadratic programming. The
process is repeated with different values of expected portfolio return,
generating the minimum risk portfolios for each value of expected return.
These minimum risk portfolios constitute the set of efficient portfolios. From
these the optimal portfolio is selected. This portfolio selection process is
known as the Markowitz model.
Merchant banker: is an institution which plays an important role in the
process of managing the public issue of securities. It helps in the issue
management process by functioning as manager, consultant, adviser, or by
rendering corporate advisory service in relation to the issue of securities.
Merchant bankers are registered with SEBI.
Money market: is the market for short term financial assets with maturities
of one year or less. Treasury bills, commercial bills, commercial paper,
certificates of deposit, etc., are the short term securities traded in the money
market. This market is known as money market because the instruments
traded in the market are considered as close substitutes for money.
Mutual fund cash ratio: is the ratio of cash maintained by mutual funds as a
percentage of their net assets on a daily or weekly or monthly basis. It is a
popular indicator of the future trend of the market. Low cash ratios are
equated with market highs indicating that the market is about to decline. On
the contrary, high mutual fund cash ratio signals a rise in prices of shares
propelled by the potential purchasing power with the mutual funds.
Naked call: is a call option written (or sold) by a party without owning the
underlying asset. If the buyer of such a call option exercises his right to buy
the asset, the writer has to purchase the asset from the market at the
prevailing market price and deliver it as the exercise price; this may involve a
loss to the writer of the naked call option.
New Issues Market: is the market in which new issues of securities are sold
by the issuing companies directly to the investors. It is also called Primary
market. When a new company is floated, its securities are issued to the public
as an Initial Public Offer (IPO). When an existing company decides to
expand its activities by issuing additional securities, these are issued in the
New Issues Market as a Follow on Public Offer (FPO). NIM does not have a
physical structure or form; all the agencies which provide the facilities and
participate in the process of selling securities to the investors constitute the
New Issues Market.
Nifty: is the market index of NSE (National Stock Exchange) composed of
50 stocks representing different sectors of the economy. The base period
price is the closing price of stocks on Nov. 3, 1995 and the base value has
been set at 1000.
Odd-lot index: is calculated by dividing odd-lot purchases (purchases of
shares in small numbers or lots) by odd-lot sales. An increase in the index
suggests relatively more buying activity and vice versa. A noticeable increase
in the index is presumed to signal a decline in the market as the market is
approaching its peak. Similarly, a noticeable decrease in the index is
presumed to signal a recovery.
Offer price: is the price at which an investor/dealer is willing to sell the
security
Open interest: refers to the number of futures contracts remaining to be
settled through delivery of the underlying asset in future on any particular
day. It gives the number of open (or outstanding) futures contracts on any
particular time or day.
Open order: is an order that remains valid till it is executed or specifically
cancelled by the investor. It is also known as good till cancelled order or
GTC order.
Optimal portfolio: is the unique portfolio among the large number of
feasible investment portfolios, giving the highest return and lowest risk. This
optimal portfolio has to be identified through a systematic process of
portfolio selection.
Option: is an agreement or contract that gives the buyer of the option the
right to buy or sell an underlying asset in the future at a pre determined price.
Option premium: is the amount (or price) paid by the buyer to buy the
option and represents the worth or value of the option. The premium can be
broken down into two parts: intrinsic value and time value. The intrinsic
value of the option is the gross profit (difference between the exercise price
and the market price of the underlying asset) accruing to the holder at any
point of time; whereas the time value is the excess of the premium prevailing
in the market over the intrinsic value of the option.
Oscillators: are mathematical indicators calculated with the help of closing
price data to identify overbought and oversold conditions in the stock market
as well as to identify the possibility of trend reversals.
OTC options: are the options traded over-the-counter. These options result
from private negotiations between the parties involved (the buyer and the
seller of the option). In these cases, the parties involved trade directly with
each other and the terms of the option contracts are tailored according to the
specific needs of the parties.
Performance margin: is also referred to as initial margin. It is the amount
to be deposited with the clearing house by both the parties to a futures
contract at the time of entering into the contract. The amount of performance
margin is fixed as a percentage of the base value of the futures contract; the
percentage may vary from contract to contract based on the risk involved in
the underlying asset.
Portfolio: is a group of securities held together as an investment. The process
of creating a portfolio is called diversification. It is an attempt to spread and
minimize the risk in investment by allocating investment funds over several
securities with different risk-return characteristics.
Portfolio analysis: is the initial phase of portfolio management process. It
consists of identifying the range of possible portfolios that can be constituted
from a given set of securities and calculating the return and risk of each such
portfolio for further analysis.
Portfolio evaluation: is the final phase in the portfolio management cycle. It
is concerned with assessing the performance of the portfolio over a selected
period of time in terms of return and risk and comparing it with objective
norms or standards of performance. It provides a feedback mechanism for
improving the entire portfolio management process.
Portfolio management: comprises all the processes involved in the creation
and maintenance of an investment portfolio. It deals specifically with security
analysis, portfolio analysis, portfolio selection, portfolio revision and
portfolio evaluation. It aims at rational allocation of funds to create the
optimal portfolio that maximizes the return and minimizes the risk.
Portfolio revision: is the process of altering the mix of securities and their
proportion in an existing portfolio in accordance with changes in the risk
return characteristics of securities in the market. New securities with
promises of high returns and low risk may be substituted for securities in the
existing portfolio which have become less attractive. The objective is to
ensure that the portfolio continues to be optimal in the ever changing
financial market.
Portfolio selection: is the process of selecting the optimal portfolio from
among all feasible portfolios. The portfolio that gives the maximum return
and minimum risk is the optimal portfolio. Portfolio theory provides the
conceptual framework and the analytical tools for selecting the optimal
portfolio.
Present value: is associated with an amount to be received in future. The
present value of a future sum is the amount to be invested now to accumulate
to that sum in the future. It is based on the premise that money has a ‘time
value’ which implies that earlier receipts are more desirable than later
receipts because the earlier receipts can be invested to earn additional returns.
Price chart: is the basic tool used by the technical analyst to study the share
price movement. It is an XY graph in which share prices are plotted with X
axis denoting the trading days or timings and the Y axis denoting the share
prices.
Primary market: is the market in which new issues of securities are sold by
the issuing companies directly to the investors. It is also called New Issues
Market (NIM). When a new company is floated, its securities are issued to the
public as an Initial Public Offer (IPO). When an existing company decides to
expand its activities by issuing additional securities, these are issued in the
primary market as a Follow on Public Offer (FPO). It does not have a
physical structure or form; all the agencies which provide the facilities and
participate in the process of selling securities to the investors constitute the
Primary market.
Private placement: is a sale of securities privately by a company to a
selected group of investors. Private placements are normally made to
institutional investors such as mutual funds, insurance companies and other
financial institutions. The terms of the issue are negotiated between the
issuing company and the investors.
Prospectus: is the offer document in a Public issue. It is a communication
from the issuing company to the investors and contains detailed information
about the company, its activities, promoters, directors, group companies,
capital structure, terms of the present issue, details of proposed project,
details regarding underwriting agreements, etc. SEBI has issued guidelines
regarding the contents of the Prospectus.
Public issue: involves sale of securities to members of the public. It is an
invitation by a company to the public to subscribe to the securities offered
through a Prospectus. It is an offer for sale of a fixed number of securities to
the public directly.
Purchasing power risk: is the variation in security returns caused by
inflation which reduces the purchasing power of the return received by the
investor. The impact of inflation is uniformly felt on all securities in the
market and hence it is classified as a type of systematic risk.
Put option: is a contract that gives the holder of the option the right to sell an
underlying asset such as a share, a stock market index, a foreign currency,
etc., at a pre determined price in the future. The person holding the option
will exercise the right to sell the underlying asset if the future price
movement of the asset is favourable to him; or else he will choose not to
exercise the right.
Random walk theory: refers to the proposition that share price movement
follows a random path and does not follow any systematic pattern. Changes
in stock prices show independent behavior and are dependent on the new
pieces of information that are received but within themselves are independent
of each other.
Red Herring Prospectus: is a document made available to prospective
investors in the public issue of securities through the book building process.
It contains most of the information regarding the operations and prospects of
the company issuing the securities but does not contain particulars regarding
the price of the securities being offered for sale and the quantum of securities
being issued. It is the Preliminary prospectus filed by a company with the
Securities Exchange Board of India.
Rematerialisation: is the process of converting securities held in electronic
form in demat accounts to securities in physical form (certificates).
Return: is the value added to the investment in the form of yield plus capital
appreciation. Yield is the dividend or interest received from the investment;
while capital appreciation is the difference between the sale price and the
purchase price of the asset involved. The return from an investment depends
upon the nature of investment, the maturity period and a host of other factors.
Rights issue: involves selling of securities to the existing shareholders in
proportion to their current holding. As per the Companies Act, when a
company issues additional shares for raising capital, the shares have to be
offered to the existing shareholders on a pro rata basis. This offer is made
through a formal letter to the existing shareholders.
Risk: is the possibility of incurring loss in a transaction. Risk is inherent in
any investment. It may relate to loss of capital, delay in repayment of capital,
non-payment of interest, or variability of returns. Risk and return of an
investment are related. Normally, higher the risk, higher is the expected
return.
Risk adjusted return: is the return per unit of risk. A risky asset such as an
equity share is expected to give a return in excess of the risk free rate of
interest. This excess return is described as risk premium which should ideally
be proportionate to the risk of the security. Risk premium per unit of risk is
known as risk adjusted return. Sharpe ratio and Treynor ratio are used as
measures of risk adjusted return.
ROC (Rate of Change Indicator): is an oscillator which measures the rate
of change of the current market price of a share as compared to the price a
certain number of days or weeks back. The ROC values may be positive,
negative or zero. Positive values of ROC indicate that the share price is rising
and is moving to an overbought condition; negative values of ROC indicate
falling prices and the building up of an oversold condition in the market.
Rolling settlement: is the procedure currently followed for settlement of
trades in stock exchanges. Trades executed on a particular day (called Trade
day, T) have to be settled after a specified number of business days or
working days. In a T+2 rolling settlement cycle, trades have to be settled on
the second business day after the Trade day.
RSI (Relative Strength Index): is an oscillator that helps to signal buying
and selling opportunities (overbought and oversold conditions) ahead of the
market movement. The RSI values range from 0 to 100. RSI values above 70
are considered to denote overbought condition and values below 30 are
considered to denote oversold condition.
Safety: refers to the certainty of return of capital without loss of money or
time. It is an important feature that an investor desires for his investments.
Screen-based trading: is the fully automated computerized mode of
securities trading where a large number of participants, geographically
separated from each other, can trade simultaneously at high speeds from their
respective locations through computer networks. The buyers and sellers can
place their orders through computer terminals into the trading system and
these orders are matched automatically according to certain pre determined
rules.
Secondary market: is the market in which securities already issued by
companies and owned by investors are subsequently traded among investors.
It is contrasted with the Primary market where securities are issued or sold by
the company to an initial set of investors. The buying and selling of these
securities then take place in the secondary market. Stock exchanges facilitate
the secondary market transactions.
Security: is the instrument through which the corporate enterprises or
governments borrow long term funds from investors. The borrowing unit
issues a certificate to the investor as evidence of the transfer of funds; this
certificate is known as corporate security or government security, depending
on who issues the certificate.
Security analysis: is the initial phase of the portfolio management process.
This step consists of examining the risk-return characteristics of individual
securities so as to estimate the intrinsic worth or value of the securities.
Security analysis helps in identifying ‘mispriced’ securities, that is, securities
whose price is higher or lower than their intrinsic value.
Securities market: the mechanism or system through which corporate
securities and government securities are created and transferred.
Sensex: is the market index of BSE composed of 30 stocks representing a
sample of large, well-established and financially sound companies selected
from different industry groups. The base year of the index is 1978−79 and the
base value is 100.
Settlement: is a part of the securities trading system. It is the process
involving delivery of the security by the seller and payment of money by the
buyer of the security. Settlement has to be completed within the specified
time period.
Sharpe ratio: is the ratio of risk premium (security return in excess of the
risk free rate of interest) to the variability of return (or risk of the security) as
measured by the standard deviation of return. It is the measure of risk
adjusted return developed by William Sharpe. It is also known as the reward
to variability ratio.
Short interest: refers to the volume of short sales in the market and is used
as an indicator of the future movements in the market. The expectation is that
short sellers must eventually cover their positions by buying the shares; their
buying activity is likely to increase the demand for shares in the future.
Short sale: is a speculative activity engaged in by speculators who anticipate
a decline in security prices in the near future. Here, the speculator agrees to
sell the security at the current market price with the intention of buying it at a
lower price when the price declines as anticipated so as to deliver the security
sold at the time of settlement of the trade. The speculator is selling a security
which he does not own or possess in the hope that he would be able to deliver
the security on the due date by buying it at a lower price within a short span
of time. He is said to take a short position with respect to the security.
Single index model: is essentially a simplification of the Markowitz model
of portfolio selection. This simplification was suggested by William Sharpe
and hence this model is also known as Sharpe model. The simplification is
in the calculation of portfolio return and risk. The consideration of covariance
of each security with each other security (in the Markowitz model) is
substituted with the relationship of each security with a market index
measured by beta. After the calculation of portfolio returns and portfolio
variances with the single index model, the set of efficient portfolios is
generated by means of the same quadratic programming routine used in the
Markowitz model. The single index model reduces substantially the data
inputs and data tabulation requirements.
SML (Security Market Line): is a straight line which expresses the
relationship between the expected return and the systematic risk (measured
by beta) of a security or portfolio. For a well diversified portfolio, the
unsystematic risk tends to become zero and the only relevant risk is the
systematic risk. Hence, the expected return of a security or portfolio should
be related to the systematic risk as measured by beta. This relationship can be
determined graphically. In an XY graph the expected returns are marked on
the Y axis and the beta coefficients are marked on the X axis. A risk free
asset as an expected return equivalent to Rf and beta coefficient of zero. The
market portfolio M (comprising of all the securities in the market) has a beta
coefficient of one and the expected return equivalent to Rm . A straight line
joining these two points is the Security Market Line. This line can be used to
determine the expected return for a security or portfolio with a given beta
coefficient.
Speculation: is a risky venture which seeks opportunities promising very
large returns within a short period of time. It is often compared to investment.
Both investment and speculation aim at good returns; the difference is in the
motives and methods.
Speculator: is a trader on the stock exchange who intends to make high
returns within a short span of time, making use of the short-term fluctuations
in security prices. He takes a long or short position on the basis on his
anticipation regarding the future movement of security prices.
Spot interest rate: is the return received on a zero coupon bond (in the form
of discount on the face value) expressed on an annualized basis.
Stag: is a speculative trader who applies for shares in the New Issues Market
just like a genuine investor, anticipating a rise in the price of the securities on
listing of the securities in the stock exchange for trading. The stag expects to
sell the allotted shares in the stock exchange at a premium, that is, at a price
which is above the issue price. A stag is said to be a premium hunter.
Stock exchange: is primarily a market for trading in securities. It is the
market in which securities already issued by companies are subsequently
traded among investors. It is an organization that provides a centralized
market mechanism for buying and selling of securities where price of
securities is determined through demand-supply mechanisms. The trading
systems and procedures in stock exchanges are regulated and continuously
monitored by Governmental agencies.
Stop order: is a market order in which the investor specifies a stop price to
limit the loss that may arise from adverse movement in the market price of
the security. In a sell order, the stop price will be below the prevailing market
price; if the market price moves down and reaches the stop price, the sell
order will be executed at the best available price to prevent further loss. In a
buy order, the stop price will be above the prevailing market price and if the
market price moves up and reaches the stop price, the buy order will be
executed at the best available price to prevent further loss. Stop order is also
known as stop loss order.
SX40: is the flagship index of MCX Stock Exchange Ltd (MCX-SX), similar
to Sensex (including 30 shares) of BSE and Nifty (including 50 shares) of
NSE. SX40 includes 40 large cap liquid stocks representing diverse sectors of
the economy. Only companies that have a minimum free float (shares that are
readily available for trading) of 10 per cent and are within the top 100 liquid
companies are included in SX40. Companies are selected for inclusion in the
index on the basis of free float weighted market capitalization. The base
value of SX40 is 10,000 and the base date is March 31, 2010.
Systematic risk: is that portion of total variability in security returns caused
by factors that are external to the company and affect a large number of
securities simultaneously. Changes in economic, political and social systems
of the country influence the performance of several companies, leading to
variability in returns of these companies.
Technical analysis: is an approach to security analysis that concentrates on
the price movements of securities. It is a study of past or historical price and
volume movements so as to predict the future stock price behavior. The basic
premise of technical analysis is that present trends are influenced by the past
trends and that the projection of future trends is possible by an analysis of
past price trends.
Trend: is the direction of movement of share prices in the market. The trend
may be described as uptrend (rising trend), downtrend (falling trend) or flat
trend (when share prices move in a very narrow range).
Trend reversal: is the change in the direction of trend of share price
movements. A share that exhibits a rising trend may start to move within a
narrow range or may begin to fall, indicating a trend reversal.
Treynor ratio: is the ratio of risk premium (security return in excess of the
risk free rate of interest) to the volatility of return (or risk of the security) as
measured by beta. It is the measure of risk adjusted return developed by Jack
Treynor. It is also known as the reward to volatility ratio.
Underwriter: is an individual or institution which gives an undertaking to
the stock issuing company to purchase a specified number of shares of the
company in the event of a shortfall in subscription to the new issue of shares.
The underwriters earn commission from the stock issuing company for this
activity.
Underwriting: is the activity of providing a guarantee to the stock issuing
company to ensure full subscription to the new issue by agreeing to buy a
specified number of shares of the company in the event of a shortfall in
subscription to the new issue. Underwriting activity is normally performed by
large financial institutions such LIC, UTI, IDBI, general insurance
companies, commercial banks and also by brokers.
Unsystematic risk: is the variability in security returns caused by internal
factors affecting only the performance of the company issuing the securities.
This risk is also known as unique risk because it affects only specific
companies or industries.
VaR (Value-at-Risk): is a metrics which calculates the maximum loss
expected (or the worst-case scenario) on an investment over a given time
period with a specified degree of confidence. It is the expected loss from an
adverse market movement with a specified probability over a period of time.
VaR is a measure of the worst possible outcome, expressed with the
probability of its occurrence. A typical VaR metrics has three parameters: the
amount of potential loss (loss amount or loss percentage), the probability of
the loss occurring (confidence level), the time frame (or horizon).
Variance-Covariance matrix: is a matrix of rows and columns wherein the
variance of each security and the covariance of each possible pair of
securities in a portfolio are shown. The entries along the diagonal of the
matrix represent the variances of securities; the other entries in the matrix
represent the covariances of the respective pairs of securities. This matrix is
set up for the calculation of portfolio variance and standard deviation.
Variation margin: is the additional amount required to be deposited in
margin account maintained by the parties to a futures contract with
clearing house when the margin balance in the account drops below
maintenance margin amount on account of variations in the price of
underlying asset.
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Wave theory: is a theory which tries to explain the behavior of the stock
market, formulated by Ralph Elliot in 1934. According to the theory, the
market moves in waves; there are impulse waves which take the market
upward and reaction or correction waves which take the market downward.
The theory is used for predicting the future price changes and in deciding the
timing of investment.
Yield to Call (YTC): is the measure of the return on a bond which is
redeemable before the full maturity period either at the option of the issuer or
the investor. It is the compounded rate of return an investor is expected to
receive from the bond purchased at the current market price and held till the
earlier date of redemption.
Yield to Maturity (YTM): is a measure of the return on bonds. It is the
compounded rate of return an investor is expected to receive from a bond
purchased at the current market price and held to maturity.
Zero coupon bond: is a special type of bond which does not specify a
coupon rate and does not pay annual interest. The return on this type of bond
is in the form of a discount on the face value of the bond offered at the time
of issue of the bond.
BIBLIOGRAPHY
Avadhani, V.A., 1997, Securities Analysis and Portfolio Management,
Himalaya Publishing, Mumbai.
Barua, Samir K., J.R. Varma and V. Raghunathan, 1996, Portfolio
Management, 1st rev. ed., Tata McGraw-Hill, New Delhi.
Blake, David, 1992, Financial Market Analysis, McGraw-Hill, London.
Dubofsky, David A., 1992, Options and Financial Futures: Valuation and
Uses, McGraw-Hill, New York.
Elton, Edwin J., and Martin J. Gruber, 1994, Modern Portfolio Theory and
Investment Analysis, 4th ed., John Wiley & Sons, New York.
Farrell, James L., Jr., 1997, Portfolio Management: Theory and Application,
2nd ed., McGraw-Hill, New York.
Firth, Michael, 1977, The Valuation of Shares and the Efficient Markets
Theory, Macmillan, London.
Fischer, Donald E. and Ronald J. Jordan, 1994, Security Analysis and
Portfolio Management, 5th ed., Prentice-Hall of India, New Delhi.
Francis, J.C., 1986, Investments—Analysis and Management, McGraw-Hill,
New York.
Hull, John C., 1996, Options, Futures, and other Derivative Securities, 2nd
ed., Prentice-Hall of India, New Delhi.
Kolb, Robert W., 1997, Understanding Futures Markets, 3rd ed., PrenticeHall of India, New Delhi.
Pistolese, Clifford, 1992, Using Technical Analysis, Vision Books, New
Delhi.
Redhead, Keith, 1998, Financial Derivatives—An Introduction to Futures,
Forwards, Options and Swaps, Prentice-Hall of India, New Delhi.
Reilly, Frank K. and Keith C. Brown, 2006, Investment Analysis and
Portfolio Management, 8th ed., Thomson Learning Inc.
Shah, Mayur, 1994, Technical Analysis, Capital Market, Mumbai.
Singh, Preeti, 1993, Investment Management, Himalaya Publishing, Mumbai.
INDEX
Activity or efficiency ratios, 95
Advantages of forward contracts, 255
American options, 295
Anticipatory surveys, 83
Arbitrage, 216, 217, 218, 292
Arbitrage pricing theory (APT), 213, 214, 215, 216, 217, 218
Assumptions of CAPM, 198
Bar chart, 134
Barometric or indicator approach, 83
Basis risk, 267
Bear, 47, 48
Bearish trend, 131, 135, 140
Beta, 61
Binomial model, 296
Black-Scholes model, 288, 309
Bombay Stock Exchange (BSE), 38
Bond duration, 121
Bond pricing theorems, 119
Bond returns, 114, 123
Bond risks, 120
Book building, 26, 27, 28
Breadth of the market, 149
Bull, 48
Bullish trend, 56, 131, 135, 137, 140
Business risk, 57, 58
Call option, 9, 271, 272, 273, 274, 275, 276, 277, 279, 280, 281, 283, 284, 285, 287, 288, 289, 290,
296, 297
Capital asset pricing model (CAPM), 7, 197, 198, 203, 204, 205, 206, 207, 208, 213, 215, 218, 238
Capital gain, 13, 16, 114, 121, 198, 227, 235, 236
Capital market, 7, 20, 26, 52, 153, 154, 197, 202
Capital market line (CML), 202, 203, 205, 208
Cash settlement, 263
Chart pattern, 136
Chicago Board Options Exchange (CBOE), 272
Clearing house, 41, 45, 46, 261, 262, 263, 264, 265, 280
Closing of futures, 263
Company analysis, 79, 91, 92, 96
Competitive market hypothesis, 159
Constant growth model, 101
Constant ratio plan, 230
Constant rupee value plan, 229
Constraints in portfolio revision, 227
Continuation patterns, 136, 139, 140
Corporate securities, 15
Cost structure, 91, 96
Coupon rate, 55, 56, 114, 119, 120, 122
Covariance, 162
Covered call, 276, 283, 284
CRISIL, 52
Current yield, 114
Day order, 44
Decay stage, 88
Deep discount bond, 3, 115
Default risk, 113, 120, 255, 264
Degree of financial leverage (DFL), 96
Degree of operating leverage (DOL), 96
Degree of total leverage (DTL), 96
Demand supply gap, 79, 89
Depositories, 38, 40, 41, 46, 49, 50
Depository participants (DPs), 49, 50
Differential return, 238, 239
Disadvantages of forwards, 255
Discount rate, 99, 102, 104, 115, 116, 117, 118
Distribution pattern, 155
Diversification, 165
Dollar cost averaging, 231
Dow theory, 130, 131
Duration, 121
Econometric model building, 84
Economic forecasting, 82, 83, 84, 85
Economy analysis, 79, 82, 85, 91
Economy-industry-company analysis, 78
Efficient frontier, 182, 183, 184, 198, 199, 202
Efficient market hypothesis (EMH), 4, 153, 154, 156, 158, 159
Efficient portfolio, 5, 182, 183, 184, 185, 197, 198, 202, 203, 205, 208
Efficient set of portfolios, 181
Elliot wave theory, 6, 141, 142
European option, 290, 295
Exchange rate, 79, 81, 190, 248, 249, 253
Exchange-traded derivatives, 249
Exercise price, 272
Expansion stage, 87
Expected return, 12, 13, 54, 58, 59, 60, 61, 65, 120, 157, 158, 161, 162, 164, 169, 170, 173, 180, 181,
182, 184, 185, 187, 197, 198, 200, 202, 203, 204, 205, 206, 207, 208, 214, 215, 216, 217, 218, 238,
239, 299
Expected return of a portfolio, 161
Expiration date, 272, 275, 276, 281, 296
Exponential moving average, 144
Fama decomposition of total return, 239
Fama’s net selectivity measure, 240
Filter tests, 155
Financial derivatives, 8, 249, 260, 271, 281
Financial intermediaries, 20
Financial market, 4, 5, 13, 18, 19, 21, 226, 227, 248, 249, 257
Financial risk, 57, 58, 253
Financial statements, 92, 95
Flags and pennants, 140
Floor trading, 42
Forecasting techniques, 82, 84, 85, 129
Forms of market efficiency, 154
Formula plans, 228, 229
Forwards, 249, 250, 255, 256, 257, 281
Functions of stock exchanges, 31
Fundamental analysis, 3, 4, 77, 78, 79, 80, 82, 91, 98, 106, 129, 150, 151, 152, 153, 156, 159
Futures, 8, 9, 249, 255, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 271, 272, 281,
287
Global minimum variance portfolio, 182, 183
Gordon share valuation model, 102, 103
Growth rates of national income, 79
Head and shoulder formation, 138, 139
Hedging, 8, 249, 255, 256, 257, 265, 266, 267, 268, 281, 284, 285
Hedging of foreign exchange risk, 253
Hedging risk, 259
Illiquidity, 256, 264
Imperfection in hedging, 267
Impulse waves, 142
Index futures, 265
Industry analysis, 79, 86, 87, 88, 89, 90, 91
Industry characteristics, 89
Industry life cycle, 87, 88
Inefficient portfolios, 181
Inflation, 12, 56, 57, 79, 80, 81, 85, 131, 190, 214
Infrastructure, 7, 35, 81, 82
Initial margin, 261
Initial public offering (IPO), 22, 31
Institutional investors, 7, 14, 20, 24, 227, 233
Inter-connected Stock Exchange of India (ISE), 35
Interest rate, 15, 56, 58, 80, 85, 98, 104, 105, 115, 118, 119, 120, 121, 122, 190, 214, 249, 271, 272,
288, 289, 309
Interest rate risk, 55, 56, 119, 120, 121, 122
Inverse head and shoulder formation, 139
Investment, 10
Investment avenues, 14, 15, 17, 18
Japanese candlestick chart, 134, 135
Jensen measure, 238, 239
Lagging indicators, 84
Lame duck, 47, 48
Leading indicators, 83
Leverage ratios, 93
Limit order, 42, 43
Limitations of Markowitz model, 184
Line chart, 130, 131, 134
Liquidity, 2, 12, 16, 20, 28, 31, 33, 35, 92, 93, 234
Liquidity ratios, 92
Listing of securities, 37
Long buy, 47, 48
Long position, 259
MACD, 147
Maintenance margin, 261
Margin system, 261
Margin trading, 48, 49, 56
Market, 20, 123
Market indicators, 148, 150
Market order, 42, 43, 44
Market risk, 55, 56, 197, 198, 204, 239, 240
Marking-to-market, 261
Markowitz model, 180, 184, 185, 186, 189
Mathematical indicators, 143
Mean-variance approach, 61
Merchant banker, 25, 27, 29, 39
Methods of floating new issues, 23
Modern portfolio theory, 7, 180
Money market, 19
Moving average, 143, 144, 147, 148
Moving average convergence and divergence (MACD), 147
Multi-index model, 189, 190, 214
Multiple growth model, 102
Multiple-year holding period, 100
Multiplier approach to share valuation, 105
Mutual fund cash ratio, 150
National Stock Exchange of India (NSE), 2, 34, 35, 51, 52, 56, 73, 260, 266, 269, 273
New issues market (NIM), 20, 21, 22, 48
Objectives of investment, 12
Odd-lot index, 150
One year holding period, 100
Open interest, 259
Open orders, 45
Opportunistic model building, 84
Optimal portfolio, 1, 5, 7, 9, 180, 183, 185, 197, 199, 226
Option premium, 272, 273, 275, 276, 277, 279, 280, 281, 282, 284, 287
Options, 8, 9, 249, 260, 271, 272, 273, 278, 279, 280, 281, 282, 283, 284, 285, 287, 288, 292, 293, 296,
309
Options contract, 9, 271, 272
Oscillators, 145
Over the Counter Exchange of India (OTCEI), 33, 34, 35
Over-the-counter derivatives, 249
Performance margin, 261
Permitted securities, 38
Pioneering stage, 87
Portfolio, 1, 2, 4, 5, 6, 7, 8, 9, 18, 61, 64, 123, 158, 161, 162, 164, 165, 166, 167, 168, 169, 170, 171,
172, 173, 180, 181, 182, 183, 184, 185, 188, 189, 190, 197, 198, 199, 200, 201, 202, 203, 204, 205,
213, 218, 227, 228, 229, 230, 231, 234, 235, 236, 237, 238, 239, 240, 241, 265, 266, 267, 268, 283
Portfolio analysis, 2, 4, 5, 161, 173, 180, 185, 186, 187, 189, 190, 226, 228, 233
Portfolio evaluation, 2, 5, 233, 235, 241
Portfolio management, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 123, 160, 161, 173, 226, 233, 241
Portfolio revision, 2, 5, 226, 227, 228, 229, 231
Portfolio selection, 2, 5, 7, 180, 183, 227, 228
Present value, 98, 99, 100, 101, 102, 103, 104,105, 115, 116, 117, 118, 121, 292, 293, 298, 299
Price chart, 6, 133, 134, 144, 146
Price limits, 258
Price-earnings ratio (P/E ratio), 105, 106
Pricing formulas, 290
Pricing of securities, 205
Primary market, 20, 22, 23, 26, 28, 29, 30, 31
Private placement, 23, 24
Profitability ratios, 93
Prospectus, 23, 24, 25, 26, 27, 28, 38
Public issue, 23, 24, 25, 26, 27, 28, 29
Purchasing power risk, 55, 56, 57
Pure discount bond, 115
Put option, 9, 272, 274, 278, 279, 280, 281, 282, 283, 285, 287, 288, 289, 290, 292, 293, 296
Random walk theory, 152, 153, 155, 156
Rate of change indicator (ROC), 145
Reaction waves, 142
Red herring prospectus, 27
Registrar to an issue, 25
Regulation of stock exchanges, 38
Relative strength index (RSI), 146
Residual analysis, 157
Return, 11
Reversal patterns, 136, 138, 139
Rights issue, 23, 26
Risk, 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 19, 28, 47, 54, 55, 56, 57, 58, 59, 61, 62, 63, 66, 88, 91,
96, 99, 102, 104, 105, 106, 113, 120, 121, 123, 158, 159, 161, 162, 163, 164, 165, 166, 167, 168, 169,
180, 181, 182, 183, 184, 186, 187, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 213, 215,
216, 218, 226, 227, 228, 233, 234, 235, 236, 237, 238, 239, 240, 241, 248, 249, 251, 252, 254, 255,
256, 257, 261, 264, 265, 266, 267, 268, 271, 278, 281, 282, 283, 284, 285, 288, 289, 293, 298, 299
Risk adjusted returns, 236
Risk free interest rate, 289
Risk of a portfolio, 162
Run test, 154
Safety, 12
Secondary market, 2, 20, 28, 30, 114
Securities, 20
Securities and Exchange Board of India (SEBI), 3, 7, 21, 22, 24, 25, 26, 27, 28, 29, 35, 37, 38, 39, 40,
49, 50, 260, 269
Securities market, 2, 9, 18, 19, 21, 28, 32, 39, 40, 51, 213, 218, 228, 229
Security analysis, 2, 3, 4, 5, 7, 9, 78, 129, 160
Security market line (SML), 203, 204, 205, 206, 207, 208
Segments of financial market, 19
Semi-strong form, 154
Semi-strong form efficiency, 156
Serial correlation test, 154
Settlement, 33, 34, 35, 40, 45, 46, 254, 255, 256, 264, 265
Share transfer agent, 25, 39
Share valuation model, 99
Sharpe ratio, 236, 237, 238
Short interest, 149
Short position, 259
Short sale, 43, 44, 47, 48, 149
Simple moving average, 143
Single index model, 157, 185, 186, 187, 189, 190
SML, 205
Speculation, 13, 14, 16, 47, 131
Spot interest rate, 114
Stag, 47, 48
Stagnation stage, 88
Standardised terms, 260
Stock exchange(s), 2, 3, 6, 9, 12, 25, 26, 30, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 44, 45, 46, 48, 50,
51, 52, 98, 260, 272
Stock exchange clearing house, 49
Stock exchange, mumbai (BSE), 2, 32, 35, 37, 51, 56, 260, 269, 272
Stock market index, 51, 61, 155, 236, 237, 265, 266
Stock options, 271
Stop limit order, 44
Stop order, 43, 44
Strike price, 272
Strong form, 154
Strong form efficiency, 158
Support and resistance, 136, 137
Support and resistance patterns, 136
Swaps, 281
Systematic risk, 55, 56, 57, 61, 62, 63, 168, 169, 187, 189, 197, 198, 203, 205, 208, 213, 218, 238
Technical analysis, 3, 4, 6, 129, 130, 133, 141, 142, 148, 150, 151, 152, 153, 154, 159
Tree of stock prices, 299
Trend reversals, 135
Treynor ratio, 237, 238
Triangles, 139
Two-stage growth model, 102
Types of financial market, 20
Types of investors, 14
Underwriting, 22, 23, 24, 27
Unsystematic, 168
Unsystematic risk, 55, 57, 58, 61, 169, 187, 188, 203, 205, 238, 239
Value-at-risk (VAR), 63, 64, 65, 66
Variation margin, 262
Weak form efficiency, 154
Yield to call (YTC), 115, 116, 117
Yield to maturity (YTM), 115, 117
Zero coupon bond, 3, 114, 115